A two-variable linear equation system would be something like:
x+y=240
2x-y=150
There are two methods to solve a system like this: substitution and elimination.
With substitution, one equation is rearranged to find the value of one of the variables and then that variable value is substituted into the equation.
Rearrange the first equation
y=240-x
Substitute the value into the second equation
2x-(240-x)=150
Solve for x.
2x-240+x=150
3x-240=150
3x=390
x=130
Lastly, plug in the value found into one of the equations, and solve for the other varaible.
130+y=240
y=110
The second method, elimination, requires the variable terms of the equations to cancel out. In the example given, the y terms will cancel out when added together. However, I will instead match the x terms together to cancel out so show the process.
Multiply the first equation by -2
-2x-2y=-480
Add the two equations together, combining like terms.
-2x-2y=-480
2x-y=150
0-3y=-330
Solve for the variable.
-3y=-330
3y=330
y=110
Lastly, plug the found variable into one of the equations to solve for the other.
2x-110=150
2x=260
x=130
So, the answer to the equation system x+y=240, 2x-y=150 is (130,110).
