Question

Solve the systems using substitution.

y = 7x - 10
y = -3
y = 2x - 15
y = 5x
-2x - 5y = -5
x = 5y - 20
A) For the first system, y = 1 and x = 2. For the second system, there is no solution. For the third system, x = 5 and y = 2.
B) For the first system, y = -3 and x = 1. For the second system, there is no solution. For the third system, x = 5 and y = 2.
C) For the first system, y = -3 and x = 2. For the second system, there is no solution. For the third system, x = 5 and y = 2.
D) For the first system, y = 1 and x = 2. For the second system, y = 3 and x = 1. For the third system, x = 2 and y = 1.

Answer 1

To solve the system of equations using substitution, we first solve one equation for one variable and then substitute that expression into the other equation. The solutions to the systems of equations are -3 and 1 for the first system, no solution for the second system, and 10 and 5 for the third system.

Step-by-step explanation:

To solve the system of equations using substitution, we will first solve one equation for one variable and then substitute that expression into the other equation. Let's solve the system step-by-step:

1. y = 7x - 10 (equation 1) and y = -3 (equation 2)

Since y is already isolated in equation 2, we can substitute -3 for y in equation 1:

-3 = 7x - 10

2. y = 2x - 15 (equation 3) and 2x - 5y = -5 (equation 4)

Let's solve equation 3 for y:

At y = 2x - 15, we can substitute 2x - 15 for y in equation 4:

2x - 5(2x - 15) = -5

By simplifying and combining like terms, we get:

2x - 10x + 75 = -5

-8x + 75 = -5

-8x = -80

x = 10

Now, substitute the value of x (10) into equation 3 to find the value of y:

y = 2(10) - 15

y = 20 - 15

y = 5

Therefore, the solutions to the systems of equations are:

For the first system, y = -3 and x = 1.

For the second system, there is no solution.

For the third system, x = 10 and y = 5.