Luttrell 2012
92
Name: ______________________
Date: _____
6h – Systems of Equations- Substitution
System is to equation as a paragraph is to a sentence. Since all the sentences in the paragraph
relate to the same idea, all the equations in a s
y
stem relate to the same variables. The solution to
a system is the ordered pair(s) that makes all the equations true.
One wa
y
of finding the solution is to graph each equation and see where the graphs intersect.
Unfortunately if the graphs intersect an
y
where but a lattice point, it is hard to determine the e
x
act
values of the ordered pair(s). Instead most mathematicians either do a substitution or an
elimination process.
E
x
ample: solve the s
y
stem of 2
x
+
y
= 3 and 3
x
- 5
y
= -2.
Step I: choose one variable in one equation to solve
y
= 3 - 2
x
Step II: Substitute the e
x
pression into other equation
3
x
- 5(3-2
x
) = -2
Step III: Simplif
y
and solve for remaining variable
3
x
- 15 + 10
x
= -2
13
x
- 15 = -2
13
x
= 13
x
= 1
Step IV: Substitute known variable into either equation
2(1) +
y
= 3
2 +
y
= 3
y
= 1
Step V: write answer
Ans: (1,1)
Solve. Sketch a graph to confirm results.
1.
x
+
y
= 3
2. 5
x
-
y
= 6
3.
y
= -
x
+ 1
x
-
y
= 2
3
x
- 2
y
= -2
y
= -3
x
+ 5
4.
y
= 3
x
+ 5
5.
x
- 4
y
= 5
6. 4
x
- 2
y
= 2
y
= 2
x
+ 2 3
x
- 4
y
= -1 -3
x
+ 2
y
= 1
