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Question
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Solve the system by substitution.

{−4.5x−2y=−12.53.25x−y=−0.75

(3 points)

Answer 1

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

Let's solve the second equation for y:
3.25x - y = -0.75

Add y to both sides of the equation:
3.25x = y - 0.75

Now, let's substitute this expression for y in the first equation:
-4.5x - 2(y - 0.75) = -12.5

Distribute the -2 to both terms inside the parentheses:
-4.5x - 2y + 1.5 = -12.5

Combine like terms:
-4.5x - 2y = -14

Now we have a new equation:
-4.5x - 2y = -14

Let's solve this equation for x:
-4.5x = -2y - 14

Divide both sides of the equation by -4.5:
x = (-2y - 14) / -4.5

Now we can substitute this expression for x in the equation -4.5x - 2y = -14:
-4.5((-2y - 14) / -4.5) - 2y = -14

Simplify:
2y + 14 - 2y = -14

The y terms cancel out:
14 = -14

This equation is not true, which means there is no solution to the system of equations by substitution.