Solving Linear Systems by Substitution - Flagler County Schools
Solving Linear Systems by Substitution - Flagler County Schools
Solving Linear Systems by Substitution - Flagler County Schools
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138 Algebra 1 Notetaking Guide • Chapter 7<br />
Example 2 The <strong>Substitution</strong> Method<br />
Solve the linear system.<br />
2x 5y 13 Equation 1<br />
x 3y 1 Equation 2<br />
Solution<br />
1. Solve for x in Equation 2 because it is easy to isolate x.<br />
x 3y 1 Revised Equation 2<br />
2. Substitute 3y 1 for x in Equation 1 and solve for y.<br />
2x 5y 13 Write Equation 1.<br />
2( 3y 1 ) 5y 13 Substitute for x.<br />
6y 2 5y 13 Distribute.<br />
11y 2 13 Simplify.<br />
11y 11 Add 2 to each side.<br />
y 1 Solve for y.<br />
3. To find the value of x, substitute 1 for y in the revised<br />
Equation 2 and solve for x.<br />
x 3y 1 Write revised Equation 2.<br />
x 3(1) 1 Substitute for y.<br />
x 4 Simplify.<br />
4. Check that ( 4 , 1 ) is a solution <strong>by</strong> substituting 4 for<br />
x and 1 for y in each of the original equations.<br />
Equation 1 Equation 2<br />
2x 5y 13 x 3y 1<br />
2( 4 ) 5( 1 ) 13 4 3( 1 ) 1<br />
8 5 13 4 3 1<br />
13 13 1 1<br />
Answer The solution is ( 4 , 1 ).
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