Question

1) Solve the following system of linear equations by either the substitution or linear combination (elimination) method. SHOW ALL WORK and write your solution as a coordinate pair. 2x+4y=20 3x+2y=26

Answer 1

I will use linear combination
to simplfiy, divide the first equation by 2 to obtain x+2y=10

eliminate x's
multiply that new first equation by -1 and add to 2nd equation

-x-2y=-10
3x+2y=26 +
2x+0y=16

2x=16
divide by 2
x=8
sub back

x+2y=10
8+2y=10
minus 8
2y=2
divide 2
y=1

so
x=8
y=1
(x,y)
(8,1)

Answer 2

solve 3x+7=26 for y
so we have 3x+y+-3x=26+3x (add-3x to both sides
y=-3x+26

-3x+26 for y in 2x+44=20
2x+4(-3x+26)=20
-10x+104=20 (simplifiy)
-10x+104+104=20+-104(add -104 to both sides)
-10x=-84
-10/-10=-84/-10
x+42/3 (that not the answer)
so you have 42/5 for x in y =-3x+26
so yis going to equal -3x+26
y=-3(42/5)+26
y+4/5 (simplify)
so you answer is 45/5 or y=4/5

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