Question

Use substitution to solve the system.
-5x+4y=-13
y=2x-7

Answer 1

To solve the system using substitution, we will substitute the expression for y from the second equation into the first equation.

Substitute y = 2x - 7 into the first equation -5x + 4y = -13:

-5x + 4(2x - 7) = -13

Simplify:

-5x + 8x - 28 = -13

Combine like terms:

3x - 28 = -13

Add 28 to both sides of the equation:

3x - 28 + 28 = -13 + 28

Simplify:

3x = 15

Divide both sides of the equation by 3:

3x/3 = 15/3

Simplify:

x = 5

Now substitute the value of x into the equation y = 2x - 7:

y = 2(5) - 7

Simplify:

y = 10 - 7

y = 3

Therefore, the solution to the system of equations is x = 5 and y = 3.