You substitute an expression for a variable, instead of a number.
Solve one of the equations for x, and then substitute the resulting expression for x into the other equation. That gives a new equation containing only y.
Alternatively, you could solve one of the equations for y, and then substitute the resulting expression for y into the other equation. That gives a new equation containing only x.
Once you have a new equation containing only one variable, you can solve it. You'll then have a number to substitute into the formula that you found for the other variable.
EG:
x + y = 4
-2x + 2y = 1
I solve the first equation for y.
y = 4 - x
I now have a formula for finding y, if I know x.
Next, I substitute this expression for y into the second equation.
-2x + 2(4 - x) = 1
Now I have an equation containing only x. I solve it.
x = 7/4
To find y, I substitute 7/4 for x into the formula for y.
y = 4 - 7/4
y = 9/4
The solution to this example system of two equations is (7/4, 9/4). :cool:
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