solve using the elimination method

Question

Step by step using elimination method:Can you please teach me how to do the elimination step by step?

11y+1=-6x

0=43-7x-4y

Answer 1

11y + 1 = -6x

0 = 43 - 7x - 4y

Here I have lined up the equals signs so we can see who is on the left and who is on the right. We can see that both of the x terms are on the right sides of their equations, so let’s try to set these up so that they are equal and opposite so we can eliminate them.

First, I can see that -6x and -7x are both negative. In order to do this elimination, I want them to be opposite signs. Before we do anything else, I’m going to pick one of the equations and flip all the signs in it so we have numbers that are opposite signs. I’m going to flip all the signs in the first equation and keep the second equation the way it is.

-11y - 1 = +6x

0 = 43 - 7x - 4y

Now that they are opposites, we can prep for elimination. I’ve lined up the x’s so we can see the numbers we are working with. We need to make 6 and 7 meet at the same number by finding their common multiple:

count by 6’s

6 12 18 24 30 36 42 48

count by 7’s

7 14 21 28 35 42 49

6 and 7 meet at 42

+6 * 7 = 42 —> multiply top equation by 7

-7 * 6 = -42 —> multiply bottom equation by 6

new equations:

-77y - 7 = 42x

0 = 258 - 42x - 24y

Now that x’s are equal and opposite = eliminate them!

Rewrite everything that’s left on both sides of the equals sign

-77y - 7 = 258 - 24y now solve algebraically for y

-77y - 7 = 258 - 24y add 7 to both sides

-77y = 265 - 24y add 24y to both sides

-53y = 265 divide by -53 on both sides

y = -5 plug back into either equation to find x

11y + 1 = -6x

11(-5) + 1 = -6x multiply 11 and -5

-55 + 1 = -6x combine -55+1

-54 = -6x divide both sides by -6

x = 9

Solution is x = 9 and y = -5

(9,-5)