4x-7y=11 -5x+2y=14 ?

4x-7y=11

-5x+2y=14

OK, I'm going to use something called the "elimination" nethod to solve this. We're going to eliminate a variable (I'll choose "x") which will set up an equation in one variable that will be easy to solve.

Note that if we multiply the top equation by 5 on both sides and the bottom equation by 4 on both sides, we get the following system:

20x - 35y = 55

-20x + 8y = 56    

.......Now, if we just add these together, note how the "x's" "disappear!!"   So we have......

-27y = 111    .... divide by -27 on both sides, and we get

y = 111/-27   =   -37/9

Now using either one of the original equations - I'll use the second one - we can substitute -37/9 for y and find x.  So we have

-5x + 2(-37/9) = 14

-5x - 74/9 = 14       ... multiply through by 9 on both sides

-45x - 74 = 126      .....add 74 to both sides

-45x = 200             .....divide by -45 on both sides

x = 200/-45 = -40/9

So there are our solutions...x = -40/9  and y = -37/9

Not very pretty, is it??   ....but, that's the way it goes sometimes !!!

If you check these in the first original equation, you will see that they "work"  (In fact, they should "work" in all the equations!!!)