Question

Note: Enter your answer and show all the steps that you use to solve this problem.
Solve the system substitution.
{-4.5x-2y=-12.5
{3.25x-y=-0.75

Answer 1

To solve this system by substitution, we will solve one equation for one variable and substitute it into the other equation.

Let's solve the second equation for y:

3.25x - y = -0.75

To isolate y, we can subtract 3.25x from both sides:

-y = -0.75 - 3.25x

To get rid of the negative sign, we will multiply both sides by -1:

y = 0.75 + 3.25x

Now that we have the value of y in terms of x, we can substitute it into the first equation:

-4.5x - 2(0.75 + 3.25x) = -12.5

Simplify:

-4.5x - 1.5 - 6.5x = -12.5

Combine like terms:

-11x - 1.5 = -12.5

To isolate x, we can add 1.5 to both sides:

-11x = -11

Divide both sides by -11:

x = 1

Now that we have the value of x, we can substitute it back into the equation for y:

y = 0.75 + 3.25(1)

Simplify:

y = 0.75 + 3.25

y = 4

Therefore, the solution to the system of equations is x = 1 and y = 4.