i need help with systems of equations with coefficients?

Question

8x-1=4y
4x=1=3y

Answer 1

2x - 2y = -4 ...... (1)
divide equation (1) by 2
ie x - y = -2 ...... (2)
-x + 3y = 6 ......(3)

Equation (2) + equation (3) will eliminate the x's

So 2y = 4
ie y = 2

Substitute in equation (3)

-x + 3*2 = 6

x = 0

check in equation (1)

2x - 2y = 0 - 2*2 = -4 YESSSSSSSSSSSSSSSS!!!

So the solution is x = 0 y = 2

Answer 2

Are you sure there shouldn't one of the 2 = in the second equation be a - or a + ?

Otherwise you get 3 equations, 4x=1 being Nr. 2 and
1 = 3y Nr. 3

Nr 2 gives x = 1/4 Nr. 3 gives y = 1/3

Filling those results in Nr. 1, you get 1 = 4/3, and that's wrong.

Answer 3

You have a typo in your second equation. I assume you mean:

8x - 1 = 4y
4x - 1 = 3y

Find the least common multiple of one of the variables so you can eliminate it. Let's eliminate x. The least common multiple is 8. So multiply the second equation by 2 and then subtract.

8x - 1 = 4y
8x - 2 = 6y
1 = -2y
y = -1/2

Now plug back in to one of the equations.

4x - 1 = 3y
4x - 1 = 3(-1/2) = -3/2
4x = -1/2
x = -1/8

So

x = -1/8
y = -1/2