What is the answer to -2x-10y equals -12 and 3x plus y equals 4?

Answer 1

-2x - 10y = -12

3x + y = 4

Simultaaneous equations.

Multiply the bottom eq'n by '10', then add. This will eliminate 'y'

Hence

-2x - 10y = -12

30x + 10y = 40 (Notice each term is multiplied by '10'.

Add

28x = 28

x = 28/28 = 1

Substituting back into either equation for 'y'.

3(1) + y = 4

3 + y = 4

y = 4 - 3

y = 1

So the answer is ( x,y) = ( 1,1).

Answer 2

x=1, y=1 looks a good guess which turns out to be correct. Add on half of the first equation to itself (so we get another "3x" equation) to get -3x-15y=-18. Now add the 2 equations to get rid of the 3x, giving you -9y=-9 or y=1. Use y=1 in either equation to get x=1.

In general you can turn one equation around to give x in terms of everything else. The substitute your expression for x into the other equation which will give you an simple equation for y only.

The method I used above found an expression for 3x rather than x alone because that's easier to substitute into the other equation.