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

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

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.x^2 + y^2 = 5 -3x + 4y = 2

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.x^2 + y^2 = 10 2x^2 - y^2 = 17

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.x^2 + y^2 = 0 2x^2 - 3y^2 = 0

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.x^2 + 2y^2 = 9 x^2 + y^2 = 25

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.3x^2 + 5y^2 = 17 2x^2 - 3y^2 = 5

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 nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.2xy + 1 = 0 x + 16y = 2

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.3x^2 - y^2 = 11 xy = 12

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose ratio is 9 to 2 and whose product is 162.

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.

Solve each problem using a system of equations in two variables. See Example 6. The longest side of a right triangle is 13 m in length. One of the other sides is 7 m longer than the shortest side. Find the lengths of the two shorter sides of the triangle.

Answer each question. Does the straight line 3x - 2y = 9 intersect the circle x^2 + y^2 = 25? (Hint: To find out, solve the system formed by these two equations.)

Answer each question. A line passes through the points of intersection of the graphs of y = x^2 and x^2 + y^2 = 90. What is the equation of this line?