Please help me solve these 2 elimination problems: 7b-5c=11, -4c-2b= -14 and 5x-8=3y, 10x-6y=18?

Answer 1

Problem 1:
7b - 5c = 11
-2b - 4c = -14

You want to eliminate a variable, so let's pick b. You need to multiply the top equation by 2 and the bottom equation by 7 so they both end up being 14 and -14...
2(7b - 5c) = 2(11)
7(-2b - 4c) = 7(-14)

When you multiply through you get:
14b - 10c = 22
-14b -28c = -98

Now just add these two equations together:
0b - 38c = -76
-38c = -76

Divide both sides by -38:
c = -76 / -38
c = 76/38
c = 2/1
c = 2

Now just plug c = 2 back into an original equation:
7b - 5c = 11
7b - 5(2) = 11
7b - 10 = 11
7b = 11 + 10
7b = 21
b = 3

So the answer is b = 3, c = 2

Problem 2:
5x - 8 = 3y
10x - 6y = 18

Again reorder them first:
5x - 3y = 8
10x - 6y = 18

First instinct says double the top equation so we have both with 10x:
2(5x - 3y) = 2(8)
10x - 6y = 18

10x - 6y = 16
10x - 6y = 18

But now we have a problem... something equals 16 and something also equals 18. This is not possible, so this system of equations is invalid.

Answer 2

For substitution, resolve the 1st equation for y, 2y=7, y=7/2. Then plug it into the different equation 5x+9(7/2)=40-one and resolve for x. Then once you get x, plug it in for y. For removal, you are able to desire to make the x or y coefficients the same. i might multiply the 2y by using 9 and the 9y in the different equation by using 2 to make the 1st equation 18y=sixty 3 and the different one 10x+18y=80 two. Then subtract the two equations, and you get your answer.