Solving Equations With Two Variables

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Solving Equations With Two Variables
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Some problems produce equations that have
variables on both sides of the equal sign.
Solving an equation with variables on both sides
is similar to solving an equation with a variable
on only one side. You can add or subtract a term
containing a variable on both sides of an
equation.
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Solving Equations With Two Variables
Solve. 4x 6 x
Step 1 Move Variable to the Same Side- Subtract
4x from both sides.
4x 4x
6 3x
-3 -3
2 x
Step 2 Isolate the Variable-Divide both sides by
3.
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Solving Equations With Two Variables
Solve. 9b 6 5b 18
Step 1 Subtract 5b from both sides.
5b 5b
4b 6 18
Step 2 Add 6 to both sides.
6 6
4b 24
4 4
Step 3 Divide both sides by 4.
b 6
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Solving Equations With Two Variables
Solve. 9w 3 5w 7 4w
Step 1 Combine like terms.
5w 4w 9w
3 ? 7
Step 2 Subtract 9w from both sides.
No solution. There is no number that can be
substituted for the variable w to make the
equation true.
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To solve multistep equations with variables on
both sides, first combine like terms and clear
fractions. Then add or subtract variable terms to
both sides so that the variable occurs on only
one side of the equation. Then use properties of
equality to isolate the variable.
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Solving Equations With Two Variables and
Fractions
y
Step 1 Combine Like Terms- Find Common
Denominator
4y
12y
15
14
y
20
20
20
20
15
Step 2 Add to both sides
16y
15
14
20
y
20
20
20
15
15

20
20
Step 3 Change y to a fraction with denominator
of 20
16y
14
y
20
20
8
20y
Step 4 Subtract to both sides
16y
14
20y
20

20
20
20
20y
20y

20
20
4y
14
Step 5 Cross Multiply


20
20
-80y -280
Step 6 Divide -80
-80 -80
7
y
2
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Try These Examples
5x 8 x
3b 2 2b 12
3w 1 10w 8 7w
10z 15 4z 8 2z - 15
y
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Summary
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it?