solving by linear combination

Question

6X+4y=7

2x-7y=-6

Answer 1

6x+4y=7

2x-7y=-6

 

to find y let's start by making x variables reciprocal equtl

 

 6x+4y=7

 -3(2x-7y=-6)

 

 6x+4y=7

-6x+21y=18....add equations

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       25y=25....divide both sides by 25 to find y

y=1

insteadvof working again for x we can easily substitute value of y in any of the equations i.e. Using equation 1

 

6x+4(1)=7

6x+4=7....subtract 4 from both sides

6x=3....to find x divide both sides by 6

x=3/6=1/2

 

now let's check it using equation 2, substitute x and y

2(1/2)-7(1)=-6

1-7=-6

-6=-6..yes

 

Answer 2

X-4y=14
3X-4y=-6

 

(X-4y=14)(-1) multiply both left and right side by -1.
3X-4y=-6

 

-X+4y=-14
3X-4y=   -6      add  this two

2x + 0 = -20

=> x = -10

Put this x=-10 back into one of the above equation and solve for y

-10-4y=14

-4y=24

y=6

does this help?