Question

Solve the system of equations below.

2x - 3y = 2
4x - y = 10
A
(7,4)
B
(5,2)
С
No solution
D
Infinitely many solutions

Answer 1

none

Explanation

A. 2x-3y=2

B. 4x-y=10

Okay.

2(7)-3(4)=2 ⇒ 14-12=2

not correct, 4(7)-(4)=10 ⇒ 28-4=24

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2(5)-3(2)= 10-6=4 not 2, incorrect

4(5)-2=10 ⇒20-2=18 incorrect.

Answer A, B, C and D are incorrect. They didn't give you the correct equations or answers. Heres why

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A. 2x-3y=2

B. 4x-y=10

1. neither equation contains an isolated variable (aka, y=x+2, y is the isolated variable). However, we can isolate -y in equation B by subtracting -4x on both sides.

Ending up with -y=10-4x

Now I like to change -y into y and it's very easy. All you need to do is:

`(-y=10-4x)/(-y)` Remember:
`(neg)/(neg)=pos, (neg)/(pos)=neg, (pos)/(neg)=neg,(pos)/(pos) =pos`

Ending up with y=-10+4x

2.Now, we can plug the expression (a phrase) -10+4x into equation A as a substitute for y and solve for x.

`2x-3(-10+4x)=2\\ 2x+30-12x=2\\ -10x+30=2\\ -10x+30-30=2-30\\ -10x=-28\\ (-10x)/(-10x) =(28)/(-10x)\\ x=-2.8`

3. Solve for y.

`2(-2.8)-3y=2\\ -5.6-3y=2\\ -5.6+5.6-3y=2+5.6\\ 3y=7.6\\ (-3y)/(-3y)=(7.6)/(-3y) \\ y=-2.5333333`

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No solution

3≠5

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Infinitely Many Solutions

3=3