Solve the following system of equations in the form of a fraction

Question

-8y+5x=4

4y-8x=7

 

What is the value of x?

Answer 1

The first thing to do is to look at your two equations and align the y variables with each other and the x variables.  You've already done that!  Then decide which variable you would like to eliminate.  The y variable seems easier since 4y can be multiplied by +2 to get 8y (the opposite of -8y).

 

      -8y  +  5x  =  4

(2)   4y  + -8x  =  7    Multiply both sides by +2

 

      -8y +   5x   =    4

       8y  + -16x  =  14   Now add together like variables.

------------------     ----

        0   + -11x  =  18    And then solve for x

 

                     x   =  18/(-11)  = -18/11

 

You could also solve this system of equations using substitution, but in this case, elimination appears to be easier.

Check your work by plugging in your answer to both equations.  Solve for y and it will be the same value in both equations.