Systems of equations

Posted on 11/11/2024, in

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Most highschoolers struggle with systems of equations, so it’s important to get this concept right! There are two ways to solve systems and with practice you will know which to use and when!

Workspace

If you have touchscreen you can use the slide show below as a place to solve questions. Click the three dots near the slide numbe, and then click on ‘Turn on pen’

Substitution

In Substitution you rewrite the equation in terms of ‘y’, then plug it in to the other equation.

Rewrite Equation in terms of ‘y’
Plug in and Solve
Find Value and plug into a equation
Solve for other value
Check by pluging in the other equation
Write as an ordered pair (x,y)

Elimination

The elimation tactic to solving systems is similar to the substitution method. In elimination you make a common element in both equations–usually by distribution–then you use it cancel the other out. Recall when solving equations that to move a term you have to preform the opposite opperation. If it’s negative, add the positive version of term to both sides; if it’s being divided (like fractions) multiply by it’s reciprocal (or just by the number). Elimination is when you use this strategy of canceling terms. Here is an example: $Elimination Example$ First identify what steps you have to take:

Rewrite the equation
Distribute to remove the ‘x’ term
Solve for ‘y’
Plug in ‘y’ and solve for ‘x’
Check by pluging in ‘y’ and ‘x’ into a equation you have not used (This is to check if you solved correctly)

$Elimination$