Standard A.REI.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Notice that y is already by itself in the first equation. We don't need to do work!
Since we know what y is equal to in the first equation, we can substitute, or replace, that into the other equation.
Notice how the second equation now has only x as its variable. When there is only one variable, we can solve for it, or isolate it. Here's all the steps:
Always choose the easiest choice. In the last example we solved for y. But solving for x in the second equation looks easier, so let's choose that.
Remember, you're always going to substitute into the other equation!
Here's the steps for how we solved:
We know what y is equal to, so let's plug that into either equation to find x. Again, choose the easiest looking equation, but either one is okay to use!
Equation #2 looks like the best one again.
Example:
We can subtract 2x on both sides of the equation of the first equation to get:
So they're the same equation.
In the first example we had:
The equations already have terms lined up but they have different numbers. However, there's a scaling factor (a number that you multiply or divide something by).
If you multiplied the second equation with a scaling factor of 4, we get:
So they're the same equation.
We can easily skip this step.
Solving systems of equations using substitution
Solving systems of equations using substitution