5x+2y=7 7x+3y=10
One of the simplest ways to solve these is to
subtract one from the other, to eliminate x or y.
Multiply the first equation by 3, and multiply the
second equation by 2.
15x + 6y = 21 14x + 6y = 20
Subtract the second equation from the first.
15x + 6y = 21
- (14x + 6y = 20)
------------------------
x = 1
Well, that was quick; and easy!
Substitute that into one of the equations.
5*(1)+2y=7
5 + 2y = 7
2y = 2
y = 1
Substitute BOTH values into the second equation.
7x+3y=10
7*(1) +3*(1) = 10
7 + 3 = 10
I guess it checks out. x is 1 and y is 1.