Solving Systems of Equations Using Elimination
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.
Strategy
- Multiply each equation so that one of the variables can cancel out
- Cancel add the functions together to cancel a variable out
- Solve for the remaining variable
- Plug in the value for the variable into one of the original equations
- Solve for last equation
Step One:
In order to solve using elimination, we have to choose a variable so that we can cancel out the a set of variables and then solve for the other.
Step Two:
We can multiply the top equation by -2 and the second equation by 3.
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When we change the equations by multiplying them, we get two new equations when the x variables cancel out.
Step Three:
You can now add the functions, and then the you are left with y as the only variable. You solve for y and get y = -5
Step Four:
Now that you know what y is, you can choose one of your original equations, plug in the value for y, and the solve for the remaining variable.
Step Five:
Since x is now the only variable that we have, you can solve for the x, and you get x = 3
Answer: One Solution at (3,-5)
Double-Check
If you type the two equations into desmos, you find that the two equations cross at what looks like (3, - 5)