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Coolmath Algebra
Systems of Equations 2x2's Lesson 2 - Solving by Substitution  
(page 1 of 4)
---- This algebra lesson explains how to solve a 2x2 system of equations by substitution.

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Let's start with a problem that's half done already...  We already know what y is:

5x + 3y = 7

y = 4

We just need to figure out what the x is.  Substitution!  Take the y guy and stick it into the first equation:

5x + 3y = 7 ... y = 4 ... plug the 4 back into the first equation for y

This gives  5x + 3 ( 4 ) = 7 .  Solve for x!

             5x + 12 = 7 ... subtract 12 from both sides, which gives 5x = -5 ... x = -1

Let's double-check that: 

5 ( -1 ) + 3 ( 4 ) = 7

So, the solution to our system is ( -1 , 4 ) .
   

Remember that this is a point where two lines intersect.

TRY IT:

Solve by substitution:

2x + 5y = -4

x = 3

Continued on the next page

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