help solve this system

Question

x-y=4

x-2y=10

 

I came up with

 

y=-4 2/3

 

Or y= -2

 

And I don't think either works back in the system:(

Answer 1

solve both equations to be in terms of x = something;

thus, x = 4 + y (add y to both sides of the equal sign) and x = 10 + 2y (add 2y to both sides of the equal sign);

once you have both equations with x = something, they can be made equal to each other, so 4 + y = 10 + 2y;

finally, solve for the value of y by subtracting y from both sides of the equation and subtracting 10 from both sides of the equation;

this makes the equation 4 + y - y - 10 = 10 + 2y -y -10, or -6 = y;

now you can solve for the value of x, using the first equation, x -y = 4 is also x = 4 + y is also x = 4 + (-6) = -2

check this with the second equation, where (-2) - 2(-6) = 10, which works out;

Answer 2

x -   y=4
x - 2y=10

subtract equation 2 from equation 1

y=-6  use this result in equation 1

x+6=4, so x=-2