How to solve system of linear equations by elimination

Say you have the system:

2x + 7y = 4

3x + 5y = -5

To solve this system using elimination, you want to cancel out either the x terms or the y terms. In this equation, it makes most sense to get rid of the x terms because they can easily be calculated as opposites. So, what we need to do is multiply each term in the first equation by 3 and multiply each term in the second equation by -2:

6x + 21y = 12 (2 * 3 = 6; 7 * 3 = 21; 4 * 3 = 12)

-6x -10y = 10 (3 * -2 = -6; 5 * -2 = -10; -5 * -2 = 10)

With that, the x terms automatically cancel out and we're left with:

21y = 12

-10y = 10

From here, we can add both equations together and get:

11y = 22

y = 2 (divide both sides by 11)

After we have one variable, we can plug it right back into either of the first two original equations; ours were 2x + 7y = 4 and 3x + 5y = -5.

So we'll take the first one and put 2 in the place of y to solve for x:

2x + 7(2) = 4

2x + 14 = 4 (multiply 7 and 2)

2x = -10 (subtract 14 from both sides of the equation)

x = -5 (divide both sides by 2)

We have that y = 2 and x = -5; there is only one more step - check your work!

Plug both values back into both original equations to check your work:

2(-5) + 7(2) = 4   =>   -10 + 14 = 4   Correct!

3(-5) + 5(2) = -5   =>   -15 + 10 = -5   Correct!

I hope this was comprehensive enough. Let me know if you have any more questions.

  or  

step-by-step explanation:

if the four friends split the cost, p, of the pizza evenly, then each friend pays one-fourth of the cost of the pizza.

the expression is   or  

asadsadsad

step-by-step explanation: