Solve the system of linear equations given below using substitution or elimination. 3x+2y=12 −x+y=11

Answer 1

Let's use the method of substitution.

We have the second equation: -x + y = 11.
Solving this equation for x, we get: x = y - 11.

Now we can substitute this expression for x into the first equation.
We have: 3x + 2y = 12.
Substituting x = y - 11, we get: 3(y - 11) + 2y = 12.
Simplifying this equation gives us: 3y - 33 + 2y = 12.
Combining like terms: 5y - 33 = 12.
Adding 33 to both sides of the equation: 5y = 45.
Dividing both sides by 5, we get: y = 9.

Now that we have the value of y, we can substitute it back into one of the original equations to solve for x.
Using the equation -x + y = 11, we have: -x + 9 = 11.
Subtracting 9 from both sides of the equation: -x = 2.
Dividing both sides by -1, we get: x = -2.

Therefore, the solution to the system of equations is x = -2 and y = 9.