10a-2b=30 3a-2b=2

Question

How to do it

Answer 1

Both equations contain 2b, so rearrange:

10a-2b=30, 2b=10a-30; 3a-2b=2, 2b=3a-2.

The RHS of the two revised equations must be equal, so:

10a-30=3a-2,

7a=28, a=4.

2b=3a-2=10a-30, so 2b=3×4-2=10×4-30=10, b=5.

SOLUTION a=4, b=5.

The same result is obtained by subtracting the original equations:

10a-2b-(3a-2b)=30-2,

10a-2b-3a+2b=28,

7a=28, a=4.

3a-2b=2, 12-2b=2, 10=2b, 5=b, b=5.