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.{2.5x−3y=−133.25x−y=−14
To solve the system by substitution, we need to choose one equation and solve it for one variable, and then substitute that expression into the other equation.
Let's solve the second equation for y:
3.25x - y = -14 [Step 1]
-y = -14 - 3.25x [Step 2]
y = 14 + 3.25x [Step 3]
Now we substitute this expression for y in the first equation:
2.5x - 3(14 + 3.25x) = -133 [Step 4]
Distribute -3 among the terms inside the parentheses:
2.5x - 42 - 9.75x = -133 [Step 5]
Combine like terms:
-7.25x - 42 = -133 [Step 6]
Add 42 to both sides of the equation:
-7.25x = -133 + 42 [Step 7]
-7.25x = -91 [Step 8]
Divide both sides by -7.25 to solve for x:
x = -91 / -7.25 [Step 9]
x = 12 [Step 10]
Now substitute x=12 into the expression for y:
y = 14 + 3.25(12) [Step 11]
y = 14 + 39 [Step 12]
y = 53 [Step 13]
Therefore, the solution to the system of equations is x=12 and y=53.