7. Systems of Equations & Matrices

In Exercises 5–18, solve each system by the substitution method. 5x + 2y = 0 x - 3y = 0

Solve each problem. See Examples 5 and 9. The sum of two numbers is 47, and the difference between the numbers is 1. Find the numbers.

Find the length and width of a rectangle whose perimeter is 40 feet and whose area is 96 square feet.

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose ratio is 4 to 3 and are such that the sum of their squares is 100.

In Exercises 1–18, solve each system by the substitution method. $\(\begin{cases}\)x + y = 1 \\(x - 1)^2 + (y + 2)^2 = 10\(\end{cases}\)$

Solve each problem. The supply and demand equations for a certain commodity are given. supply: p = 2000/(2000 - q) and demand: p = (7000 - 3q)/2q.

Find the equilibrium demand.

Solve each problem. The supply and demand equations for a certain commodity are given. supply: p = √(0.1q + 9) - 2 and demand: p = √(25 - 0.1q).

Find the equilibrium price (in dollars).

Solve the system

In Exercises 29–42, solve each system by the method of your choice. $\(\begin{cases}\)x^2 + (y - 2)^2 = 4 \\(\x\)^2 - 2y = 0\(\end{cases}\)$

Solve each problem. Find the equation of the line passing through the points of intersection of the graphs of x² + y² = 20 and x² - y = 0.

Solve each problem. See Examples 5 and 9. At the Berger ranch, 6 goats and 5 sheep sell for \$305, while 2 goats and 9 sheep sell for \$285. Find the cost of a single goat and of a single sheep.

In Exercises 1–18, solve each system by the substitution method. $\(\begin{cases}\)xy = 3 \\(\x\)^2 + y^2 = 10\(\end{cases}\)$

In Exercises 1–18, solve each system by the substitution method. $\(\begin{cases}\)y = x^2 - 4x - 10 \\(\y\) = -x^2 - 2x + 14\(\end{cases}\)$