7. Systems of Equations & Matrices

In Exercises 1–18, solve each system by the substitution method.$\begin{cases}x^2 + y^2 = 25 \\x - y = 1\end{cases}$

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

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

Solve each system by the substitution method.

$\begin{cases}x + y = 2 \\y = x^2 - 4\end{cases}$

The perimeter of a rectangle is 26 meters and its area is 40 square meters. Find its dimensions.

In Exercises 25–35, solve each system by the method of your choice. This is a piecewise function, refer to textbook problem.

Solve each system by the method of your choice.

$\{\begin{array}{c}5y=x^2-1\\ x-y=1\end{array}$

In Exercises 25–35, solve each system by the method of your choice. This is a piecewise function, refer to textbook problem.

Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence. The following nonlinear system has two solutions, one of which is (3,____).

x + y = 7

x² + y² = 25

Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence. The following nonlinear system has two solutions, one of which is (___, 3).

2x + y = 1

x² + y² = 10

Answer each of the following. When appropriate, fill in the blank to correctly complete the sentence. If we want to solve the following nonlinear system by substitution and we decide to solve equation (2) for y, what will be the resulting equation when the substitution is made into equation (1)?

x² + y = 2 (1)

x - y = 0 (2)

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose sum is 17 and whose product is 42.

Solve each problem using a system of equations in two variables. See Example 6. Find two numbers whose squares have a sum of 100 and a difference of 28.

Verify that the points of intersection specified on the graph of each nonlinear system are solutions of the system by substituting directly into both equations.

2x² = 3y + 23

y = 2x - 5

Verify that the points of intersection specified on the graph of each nonlinear system are solutions of the system by substituting directly into both equations.

y = 3x²

x² + y² = 10