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. x+3.5y=9.5 2x+2y=14

Answer 1

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

Let's solve the first equation, x + 3.5y = 9.5, for x:
x = 9.5 - 3.5y

Now we will substitute this value of x into the second equation, 2x + 2y = 14:
2(9.5 - 3.5y) + 2y = 14

Distribute the 2:
19 - 7y + 2y = 14

Combine like terms:
-5y + 19 = 14

Subtract 19 from both sides:
-5y = 14 - 19
-5y = -5

Divide by -5:
y = -5/-5
y = 1

Now substitute this value of y back into the first equation to find x:
x + 3.5(1) = 9.5
x + 3.5 = 9.5
x = 9.5 - 3.5
x = 6

Therefore, the solution to the system of equations is x = 6 and y = 1.