find the solution of this system of equation

WYZANT.COM
CREATE FREE ACCOUNT
Sign In

Access thousands of free resources from expert tutors

Comment on posts and interact with the authors

Ask questions and get free answers from tutors

View videos, take interactive quizzes, and more!

find the solution of this system of equation

Tutors, please sign in to answer this question.

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

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

{-5x+y=-7}

{-6x-y=7}

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+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)

-11x+7=7

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

-11x=0

-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)

x=0

Now we will solve for y...

I will use what I know and plug it in.

-6x-y=7

-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

x=0

Now let's check our answer

-5x+y=-7

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

-7=-7 yes it worked

-6x-y=7

-6(0)-(-7)=7

7=7 yes it worked

X=0

Y=-7

- Algebra 903
- Math 1329
- Equations 124
- Algebra 2 488
- Word Problem 401
- Probability 133
- Algebra Equation 117
- Fractions 84
- Graphing 70
- Word Problems 64

## Comments

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.

Comment