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Question

Solve the system by substitution.

{−4.5x−2y=−12.5
3.25x−y=−0.75
(3 points)

Answer 1

To solve the system by substitution, we need to solve one equation for one variable and then substitute this expression into the other equation.

First, let's solve the second equation for y:
3.25x - y = -0.75
y = 3.25x + 0.75

Now we can substitute this expression for y into the first equation:
-4.5x - 2(3.25x + 0.75) = -12.5
-4.5x - 6.5x - 1.5 = -12.5
-11.5x - 1.5 = -12.5

Next, let's isolate the x variable:
-11.5x = -12.5 + 1.5
-11.5x = -11
x = -11 / -11.5
x = 0.9565 (rounded to four decimal places)

Now that we have the value of x, we can substitute it back into the expression for y in the second equation:
y = 3.25(0.9565) + 0.75
y = 3.1 + 0.75
y = 3.85

The solution to the system of equations is x = 0.9565 and y = 3.85.