# Solving a System of Equations Using Substitution

This video shows how to solve using substitution.
To solve using substitution, set both equations equal to each other if they both equal y.
This can only be done if you have one equation in terms of a variable.
By having an equation equal to variable, you can plug into the other equation in terms of that variable, and solve.
If an equation is NOT already equal to a variable, then you would have to isolate a variable for the equation(s), so that it can be plugged into the other equation.
After that, you solve for the missing variable and plug it back into one of the original equations to get the value of the second variable.
The x and y-values are the coordinates for the point of intersection of the two lines.
To check this, plug both x and y-values into an original equation and simplify to see if it holds true.
For example:
$y=x+1$
$y=2x-1$
Rewrite this after plugging in 2x-1 for where we see y in the first equation. So:
$2x-1=x+1$
After solving, we find that x=2.
Then plug in 2 for x in either equation to solve for the y value.
$y=2(2)-1$
$y=3$
Therefore, the solution is (2,3).

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Used by students across the country. Pre-Algebra, Algebra I, Geometry, & Algebra II