SOLUTION: Would someone please help me? I am absolutely desparate and stuck on these two problems. I would appreciate any help I can get. Thanks Solve by the elimination method 5r-6s=4

Question 342122: Would someone please help me? I am absolutely desparate and stuck on these two problems. I would appreciate any help I can get. Thanks
Solve by the elimination method
5r-6s=4
6r+5s=17
Solve by the substitution method
6x+7y=8
x=16-3y
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Solve by the elimination method
5r-6s=4
6r+5s=17
We want to multiply one or both equations with values that will make the coefficient of one of the variables the same
In this system multiply the 1st equation by 5 and the 2nd equation by 6, we have:
25r - 30s = 20
36r + 30s = 102
-----------------Adding these eliminates s, find r
61r + 0 = 122
r =
r = 2
Use the original 2nd equation to find s, replace r with 2
6(2) + 5s = 17
12 + 5s = 17
5s = 17 - 12
5s = 5
s = 1
:
Check solution by replacing r and s in the 1st original equation
5(2) - 6(1) = 4
10 - 6 = 4; confirms our solution of r=2, s=1
:
:
Solve by the substitution method
Here we use one of the equation to substitute in the other equation
6x+7y=8
x=16-3y
We know that x = 16-3y, substitute (16-3y) for x in the 1st equation
6(16-3y) + 7y = 8
96 - 18y + 7y = 8
-18y + 7y = 8 - 96
-11y = -88
11y = 88; multiplied both sides by -1
y =
y = 8
;
Find x using the 2nd equation, replace y with 8:
x = 16 - 3(8)
x = 16 - 24
x = -8
:
Check solution in the 1st equation replacing x and y
6(-8) + 7(8) = 8
-48 + 56 = 8; confirms our solution of x=-8, y=8
;
:
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