Use the graph to identify the solution to the system of equations or identify that the system has 0 0 or infinitely many solutions. If there is a solution, check that the point satisfies both equations.

Everybody. So now that we have understand how to solve system of equations by graphing, let's take a look at our first practice problem here. So we're told to use the graph to identify the solution to the system of equations or identify that the system has zero or infinitely many solutions. If you remember, the solution to a system of equations, the way you find that graphically, is just the point where the two lines intersect. Alright? If they don't intersect, it's zero. And if they're the same line, it's infinitely many solutions. Now if there is a solution, what this question asks us to do, let's go one step further and check that the point actually satisfies both of those equations. Okay? So let's go ahead and get started here. We can see that these two lines are sort of going to crisscross like this, and they are going to intersect. And remember that the solution is basically that point where they intersect, which is going to be right over here. Alright? Now the coordinate for that is going to be zero comma 3, and that's really the answer. The answer is that the solution to the system is zero comma three. Now what ends up happening here is typically sometimes if you're drawing these things on a hand drawn graph, sometimes you can draw the lines incorrectly. And so maybe what you've drawn is maybe not actually the point zero comma three. It just looks like it. So we're going to go ahead and check the point satisfies both of those equations so we can really, really be sure that that's the correct answer. Okay? So I'm going to start off with this equation or this line that goes sort of up towards the top right, that positively sloped line. And I'm going to go ahead and write out the equation for this in slope intercept form. So that's y equals mx plus b. So I'm just going to write y equals something times x and then plus something else. So the second number is always just the point where it crosses the y axis. That's the y intercept. That's what goes at the end. And clearly, we can see here that the y coordinate where it crosses the y axis is three. Now, I want to be really clear here. It's not three because that's the point where the two lines cross. It's three because that's where this line crosses the y axis. Alright. That's the reason it's three. Okay? So now in order to get the slope, we just pick any two points across this line, then we just figure out the rise over the run. Okay? So I'm gonna go ahead and pick this point and this one, but you could use really any two points. You're just trying to figure out what's the rise over the run. So I have to go one up and then one over, one up and one over, and so on and so forth. So in other words, the slope is basically just one over one. In other words, the slope of this line is just one. So we have y equals one x plus three. You don't have to write that one, but I'll just leave it there. Okay? Now we're gonna do the same exact thing for this line over here, the one that goes down towards the bottom right. So we're going to do the same exact thing. What's the y intercept, the place where it crosses the y axis? It's actually the same. It's still plus three. Again, not because that's where these two lines cross each other, but that's where this line crosses the y axis over here. All right? So now it's the slope. We just pick any two points across that line, and we just compute the rise over the run. Alright? So I have to go one down over, one down and then one over, one down and then one over. And then you know when you when you go down, it's gonna be a negative one over one, negative one over one. So in other words, the slope of this line is negative x plus three. Okay? Now we've written both of these equations. We can go ahead and check that point actually satisfies those those equations. So we're gonna go ahead and check, again, the point zero comma three. You just plug the x coordinate in for the x, the y coordinate in for the y, and then so on and so forth. Alright? So we can see here is three, does that actually equal one times zero plus three? It's sort of like a question mark there for that equal sign. And you can see that one times zero is just going to be zero, leaving you with just positive three on both sides of the equations. So that's going to be true. That's going to be a true statement. If you do the same exact thing over here, you're going to just check the points zero comma three, and you're going to end up with three. Does that equal negative one times zero plus three? Do the same exact thing, right? So your negative one times zero doesn't matter, it's still just zero. So that just goes away. And you have positive three on both sides. So it definitely ends up being a true statement. So because this point satisfied both of those equations, that's the only point that's going to satisfy this system of equations here. And that's your answer. So again, let me know if you have any questions, and if not, let's move on.

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1. Whole Numbers1h 55m

Multiplying Whole Numbers
46m

Dividing Whole Numbers
21m

Long Division
36m

Exponents
10m

2. Integers1h 7m

Introduction to Integers
16m

Multiplying Integers
24m

Exponential Expressions
10m

Dividing Integers
16m

3. Introduction to Solving Equations and Problem Solving Coming soon

4. Fractions1h 29m

Intro To Fractions and Mixed Numbers
44m

Simplifying Fractions
45m

5. Decimals1h 20m

Introduction to Decimals
26m

Rounding Decimals
12m

Adding And Subtracting Decimals
41m

6. Ratio, Proportion, and Percent2h 1m

Ratios and Rates
35m

Proportions
33m

Solving Percent Problems With Equations
16m

Applications of Percent
36m

7. Graphing and Introduction to Statistics Coming soon

8. Geometry49m

Square Roots and The Pythagorean Theorem
29m

The Circle
20m

9. Measurement Coming soon

10. Linear Equations and Inequalities6h 29m

The Distributive Property
17m

Evaluating Expressions
15m

Review: Addition and Subtraction Properties of EqualityBonus
41m

Review: Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Introduction to Problem Solving
37m

Formulas
21m

Review: Percent Problem Solving
59m

Mixture Problem Solving
43m

Linear Inequalities in One Variable
46m

11. Graphing Linear Equations and Inequalities4h 58m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

Linear Inequalities in Two Variables
28m

Introduction to Relations and Functions
57m

Function Notation
15m

12. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

13. Exponents and Polynomials3h 55m

Review: Evaluating Exponents
29m

The Product Rule
10m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

The Quotient Rule
13m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

14. Factoring Polynomials2h 42m

Factoring by Greatest Common Factor & Grouping
37m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
20m

Sum & Difference of Cubes
12m

Quadratic Equations & Applications
41m

15. Rational Expressions and Equations3h 40m

Simplifying Rational Expressions
39m

Multiplying And Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

Direct & Inverse Variation
27m

16. Roots and Radicals2h 46m

Introduction to Radical Expressions
47m

Simplifying Radical Expressions
46m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
53m

17. Quadratic Equations1h 55m

The Square Root Property
17m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
30m

12. Systems of Linear Equations

Solving Systems of Linear Equations by Graphing

Prealgebra & Beginning Algebra

12. Systems of Linear Equations

Solving Systems of Linear Equations by Graphing

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Multiple Choice

Use the graph to identify the solution to the system of equations or identify that the system has $0$ or infinitely many solutions. If there is a solution, check that the point satisfies both equations.

$open paren 0 comma 3 close paren$

$open paren negative 3 comma 3 close paren$

No Solution

Infinitely many solutions

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Use the graph to identify the solution to the system of equations or identify that the system has 00 or infinitely many solutions. If there is a solution, check that the point satisfies both equations.

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Use the graph to identify the solution to the system of equations or identify that the system has $0$ or infinitely many solutions. If there is a solution, check that the point satisfies both equations.