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Question

Solve the system substitution.

{(-4.5x-2y=-12.5),(3.25x-y=-0.75)

Answer 1

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

Let's start by solving 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 make the coefficient of y positive, we can multiply both sides by -1:
y = 0.75 + 3.25x (Equation 1)

Now, we will substitute this expression for y into the first equation:
-4.5x - 2(0.75 + 3.25x) = -12.5
To simplify, we distribute the 2:
-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 = -12.5 + 1.5
-11x = -11
Divide both sides by -11 to solve for x:
x = -11 / -11
x = 1

Now that we have the value of x, we can substitute it back into Equation 1 to find y:
y = 0.75 + 3.25(1)
y = 0.75 + 3.25
y = 4

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