To solve this system of equations, we can use the method of substitution or elimination. Let's solve it using the substitution method:
Step 1: Solve one equation for one variable in terms of the other variable.
From the second equation:
x - 2y = 11
We can rearrange this equation to solve for x:
x = 2y + 11
Step 2: Substitute the expression for the solved variable in the other equation.
Now we substitute the expression for x in the first equation:
-7(2y + 11) - 2y = -13
Step 3: Solve the resulting equation for the remaining variable.
We simplify the equation:
-14y - 77 - 2y = -13
-16y - 77 = -13
-16y = 77 - 13
-16y = 64
y = 64 / -16
y = -4
Step 4: Substitute the value of y back into one of the original equations to solve for x.
Using the second equation:
x - 2y = 11
x - 2(-4) = 11
x + 8 = 11
x = 11 - 8
x = 3
Step 5: Check the solution.
Plug the values of x and y into the first equation:
-7x - 2y = -13
-7(3) - 2(-4) = -13
-21 + 8 = -13
-13 = -13
The solution to the system of equations is x = 3, y = -4.
−7x−2y=−13 x−2y=11
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