Final answer:
To solve the system of equations by substitution, solve one equation for one variable and substitute the expression into the other equation. Then solve for the remaining variable and substitute the value back into one of the original equations. x = 6 and y = -28.
Step-by-step explanation:
To solve the system of equations by substitution:
Step 1: Solve one of the equations for one variable in terms of the other.
Step 2: Substitute the expression obtained in Step 1 into the other equation.
Step 3: Solve the resulting equation for the remaining variable.
Step 4: Substitute the value found in Step 3 back into one of the original equations to find the value of the other variable.
Using the given system of equations:
First, solve the first equation for y:
y = -6x + 8
Substitute this expression for y into the second equation:
7x + 2(-6x + 8) = -14
Simplify and solve for x:
7x - 12x + 16 = -14
-5x + 16 = -14
-5x = -30
x = 6
Substitute x = 6 back into the first equation to find y:
y = -6(6) + 8
y = -36 + 8
y = -28
Therefore, the solution to the system of equations is x = 6 and y = -28.