Question

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Solve the system substitution.
-4.5x-2y=-12.5
3.25x-y=-0.75

Answer 1

To solve the system of equations by substitution, we can solve one equation for one variable and substitute it into the other equation.

Let's solve the first equation for x:
-4.5x - 2y = -12.5
We can isolate x by moving the -2y term to the other side of the equation:
-4.5x = -12.5 + 2y
Divide both sides of the equation by -4.5:
x = (-12.5 + 2y) / -4.5

Now we substitute this expression for x into the second equation:
3.25x - y = -0.75
Replace x with the expression we found: (-12.5 + 2y) / -4.5
3.25((-12.5 + 2y) / -4.5) - y = -0.75

Now we can simplify this equation and solve for y:

First, distribute 3.25 to (-12.5 + 2y):
((-12.5 * 3.25 + 2y * 3.25) / -4.5) - y = -0.75

Simplify the numerator:
((-40.625+6.5y) / -4.5) - y = -0.75

Now, multiply through by -4.5 to clear the fraction:
-40.625 + 6.5y + -4.5y = -0.75 * -4.5

Simplify the right side:
-40.625 + 2y = 3.375

Move -40.625 to the other side:
2y = 3.375 + 40.625

Simplify the right side:
2y = 44

Divide both sides by 2 to solve for y:
y = 22

Now substitute this value for y into the first equation to find x:
-4.5x - 2(22) = -12.5

Simplify:
-4.5x - 44 = -12.5

Move -44 to the other side:
-4.5x = 44 - 12.5

Simplify the right side:
-4.5x = 31.5

Divide both sides by -4.5 to solve for x:
x = 31.5 / -4.5

Simplify:
x = -7

So the solution to the system of equations is x = -7 and y = 22.