Marvelous
Math
There
are several ways to solve Systems of Equations.
This
page shows you how, using either substitution or linear combination. It
also gives you an example of a linear equation in a word problem.
| Using Substitution... |
The
Problem: |
| #1)
You cannot solve the equation with both variables in it, you must SUBSTITUTE
the "y=" equation into the other one. -->
#2) Use the distributive property at your parentheses. #3) Combine like terms. Solve the equation. #4) Use the x that you just solved for in the first equation to find the y in the second. Then solve the second equation. Put into coordinates. |
Step #1) 3x - 2(5 - 4x) = 12 Step
#2) Step
#3)
(x,y) = (2,-3)
|
| Using Linear Combination... |
The Problem: |
|
#1) The negative "x" and the positive "x" cancel each other out. Cross them both out and then combine the rest of the two equations together. #2) Once you get what "y" equals, you can plug this into one of the equations and solve it for "x". #3) Once you get both the "x" and the "y" put it into coordinates such as (x,y). |
Step
#1) -2y + 3y = 6 - 4 y = 2
Step #2)
Step #3) |
| Word Problem... |
The
Problem: |
| #1)
Set up the first part of the problem into an equation. "x" will be the
larger number and "y" will be the smaller.
#2)
The second step says to multiply the larger number, "x", by 3 and the smaller
number, "y", by 9.
#3) Use what you have for "x" to plug into the original equation to find "y". Solve that equation. #4) Now you have solved for "y". Use this to plug into the equation to solve for "x". Put into the coordinates. |
Step #1) x - y = 16 Step
#2) Step
#3) Step
#4) |
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