7. Systems of Equations & Matrices

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.

$y=6x+x^2$

$4x-y=-3$

In Exercises 5–18, solve each system by the substitution method. $\(\begin{cases}\)x + 3y = 8 \\(\y\) = 2x - 9\(\end{cases}\)$

Solve each system by elimination. In systems with fractions, first clear denominators.

2x - 3y = -7

5x + 4y = 17

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.

$x^2+y^2=02$

$x^2-3y^2=0$

Determine whether the given ordered pair is a solution of the system. $(-3,5)$

$\(\begin{cases}\)9x + 7y = 8 \\8x - 9y = -69\(\end{cases}\)$

Solve each system. (Hint: In Exercises 69–72, let $1/x=t$ and $1/y=u$.)

$\frac{2}{x}+\frac{3}{y}=18$

$\frac{4}{x}-\frac{5}{y}=-8$

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.

$y=x^2+6x+9$

$x+2y=-2$

Solve each system of equations. State whether it is an inconsistent system or has infinitely many solutions. If a system has infinitely many solutions, write the solution set with x arbitrary.

5x - 5y - 3 = 0

x - y - 12 = 0

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.

$5x^2-2y^2=25$

$10x^2+y^2=50$

Solve each problem. Find all values of b such that the straight line 3x - y = b touches the circle x² + y² = 25 at only one point.

Solve each system by substitution.

4x + 3y = -13

-x + y = 5

Determine whether the given ordered pair is a solution of the system. $(2,3)$

$\(\begin{cases}\)x + 3y = 11 \\(\x\) - 5y = -13\(\end{cases}\)$

In Exercises 19–28, solve each system by the addition method. $\(\begin{cases}\)y^2 - x = 4 \\(\x\)^2 + y^2 = 4\(\end{cases}\)$

In Exercises 49–50, solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0, b ≠ 0 5ax + 4y = 17 ax + 7y = 22

In Exercises 31–42, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 3x - 2y = − 5 4x + y = 8