Hi, there--

Problem:
Use Cramer's Rule to solve this system of linear equations: 
x + 2y = -7
2x = 4 + 5y

A Solution:

Cramer's Rule uses the determinant of the coefficient matrix related to this system of 
equations to find the solution.

First, set up the 2 x 2 coefficient matrix. Write both equations in Ax + By = C form.

x + 2y = -7
2x -5y = 4

Now set up the 2 x 2 matrix using the coefficients of the x and y terms.


To find the determinant D, we use the formula,



For your system we have



Now we find two more determinants,  and .

For , we substitute the values on the right side of our equations for the left column of the coefficient matrix.



For , we substitute the values on the right side of our equations for the right column of the coefficient matrix.



Cramer's Rule states that for the solution to our system of equations (x,y)

 
and


So, the ordered pair (-3,-2) is the solution to your system of equations.

Let's check this point in our original equations to be sure.
x + 2y = -7
(-3) + 2(-2) = -7
-3 - 4  = -7
-7 = -7 
CHECK!

2x = 4 + 5y
2(-3) = 4 + 5(-2)
-6 = 4 - 10
-6 = -6 CHECK!

That's it. I hope this helps,
Mrs. Figgy