# Can you complete this question?

6x + 2y = 2

5x - 7y = 6 < Can you solve this?

It's the only GCSE algebra question I didn't get during my mock test! I honestly can't work it out.

P.s. Don't use internet :L

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Really? Hmm... I'll post my working out, tell me where it's wrong.
(6x+2y=2) = (6x=2-2y) 6x/6=x 2/6=1/3 -2y/6=-1/3y
(5x - 7y = 6) = (-7y = 6-5x ) -7y/-7=y 6/-7=-6/7 -5x/-7=5/7x
y=-6/7+5/7(1/3-1/3y) 5/7(1/3-1/3y)= 26/21y = 13/21 (26/21y)/(26/21)=y (-13/21)/(26/21)= -1/2
x=1/3-1/3(-1/2) 1/3(-1/2)=-1/6 1/3-1/3 X=1/2
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My working: Rearrange 6x + 2y = 2 -> 2y = 2 - 6x -> y = 1 - 3x Substitute y = 1 - 3x into 5x - 7y = 6 -> 5x - 7(1-3x) = 5x - 7 + 21x = 6 -> 5x + 21x = 13 -> 26x = 13 -> x = 1/2 Substitute x = 1/2 into 6x + 2y -> 3 + 2y = 2 -> 2y = -1 -> y = -1/2 Check by substituting x and y values into both original equations: 5(1/2) -7(-1/2) = 5/2 + 7/2 = 12/2 = 6 which is correct 6 (1/2) + 2(-1/2) = 6/2 - 2/2 = 3 - 1 = 2 which is correct X=.5 Y=-.5 To complete this, multiply the first equation by 7 and the bottom equation by 2 so as the two y's will cancel out. You will then be left with 52x=26 (after the two equations were combined) which will lead to the sum.of x being .5. Fill x in one equation as .5 and solve. You should be left with y=-.5 |