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-5x+y=-7 and -6x-y=7

find the solution of this system of equation


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2 Answers

Skyrie did an excellent job of creating a step by step solution, and she has my vote. Having said that, there is a shortcut.

-5x + y = -7

6x - y = 7

Just add the two equations. The y's cancel out. -7 and 7 also cancel out.

-5x + y + 6x - y = x

x = -7 + 7 = 0

-5(0) + y = 0 + y = y = -7

Check: 6x - y = 6(0) - (-7) = 0 + 7 = 7


I love the technique you used I never thought of it that way. I would love to use that technique if you do not mind.

This is a system of equation. I will go over it step by step so that you will understand what is going on.



I would first give (y) a meaning, so then I can use it for substitution later. I will use the equation (-5x+y=-7).


+5x     +5x    <==== I added 5x on both sides so that I can have y alone

  y= -7+5x    <===== The y is now equal to -7+5x, I will use this for my other equation (-6x-y=7).

I will substitute y from -6x-y=7 and replace it with my new equation -7+5x.

-6x-(-7+5x)=7  <=== remember to make the equation nice and neat for you to understand, fix your       negative and positive signs.

-6x+7-5x=7 <==== when you multiply two negatives it makes a positive, however, multiplying a negative and a positive makes a negative.

(-6x-5x)+7=7  <=== combine like terms

-11x+7=7   <=== remember (keep switch change) you keep -6x switch the negative to a positive and change the positive 5 to a negative 5. ( This only applies when you are subtracting or adding number)


      -7=-7  <===  I subtracted 7 on both sides so that I can have x alone


-11     -11 <==== I divided -11 on both sides ( 0 divided by any number equals to 0, but it is impossible to divide a number by 0 it would be undefined check on you calculator)


Now we will solve for y...

I will use what I know and plug it in.


-6(0)-y=7 <=== x=0 remember

-y=7 <=== 0 times any number equal 0

-1   -1 <=== when a variable exist but it has no number in front of it there is an imaginary 1 in front of the variable.

y= -7


Now let's check our answer



-7=-7 yes it worked 



7=7 yes it worked