INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith

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### More Than One Variable

• Some equations involve more than one variable, say x and y. Sometimes you are asked to solve such an equation for a specified variable, such as y.
• To solve such equations, isolate the variable you are solving for using the standard techniques.
• Sometimes, in more complicated equations, you need to use the distributive property to isolate the variable.
• An important application of this type of problem is to solve a given geometric or scientific formula involving two or more variables for a specified variable.

### More Than One Variable

Solve for y:4x − 11y = 15
• 4x − 11y − 4x = 15 − 4x
• − 11y = 15 − 4x
• [( − 11y)/( − 11)] = [(15 − 4x)/( − 11)]
y = − [(15 − 4x)/11]
Solve for a:11a + 12b − 6 = 14
• 11a + 12b − 6 + 6 = 14 + 6
• 11a + 12b = 20
• 11a + 12b − 12b = 20 − 12b
• 11a = 20 − 12b
• [11a/11] = [(20 − 12b)/11]
a = [(20 − 12b)/11]
Solve for t:s − 8st = 3t − 7
• s − 8st − 3t = 3t − 7 − 3t
• s − 8st − 3t = − 7
• s − 8st − 3t − s = − 7 − s
• − 8st − 3t = − 7 − s
• t( − 8s − 3) = − 7 − s
• [(t( − 8s − 3))/(( − 8s − 3))] = [( − 7 − s)/(( − 8s − 3))]
t = [( − 7 − s)/(( − 8s − 3))]
Solve for v:4u + 3uv = v − 1
• 4u + 3uv − v = v − 1 − v
• 4u + 3uv − v = − 1
• 4u + 3uv − v − 4u = − 1 − 4u
• 3uv − v = − 1 − 4u
• v(3u − 1) = − 1 − 4u
• [(v(3u − 1))/((3u − 1))] = [( − 1 − 4u)/(3u − 1)]
v = [( − 1 − 4u)/(3u − 1)]
Solve for n:[(n + m)/(n − m)] = 4m
• (n − m) ×[(n + m)/(n − m)] = 4m(n − m)
• n + m = 4m(n − m)
• n + m = 4mn − 4m2
• n + m − 4mn = 4mn − 4m2 − 4mn
• n + m − 4mn = − 42
• n + m − 4mn − m = − 4m2 − m
• n − 4mn = − 4m2 − m
• n(1 − 4m) = − 4m2 − m
• [(n(1 − 4m))/((1 − 4m))] = [( − 4m2 − m)/((1 − 4m))]
n = [( − 4m2 − m)/((1 − 4m))]
Solve for c:
[(c − d)/2c] = 5d
• 2c( [(c − d)/2c] ) = 5d(2c)
• c − d = 5d(2c)
• c − d = 10dc
• c − d + d = 10cd + d
c = 10cd + d
Solve for k:
[(j − k)/(j + k)] = 3j
• (j + k)( [(j − k)/(j + k)] ) = 3j(j + k)
• j - k = 3j(j + k)
• j − k = 3j2 + 3k
• j − k − j = 3j2 + 3k − j
• − k = 3j2 + 3k − j
• k = − (3j2 + 3k − j)
k = − 3j2 − 3k + j
Solve for r:
16r − 12s = 48
• 16r − 12s + 12s = 48 + 12s
• 16r = 48 + 12s
• [16r/16] = [(48 + 12s)/16]
• r = [(48 + 12s)/16] = [(12 + 3s)/4]
r = [(12 + 3s)/4]
Solve for u:2u − 7uv = 5v + 9
• u(2 − 7v) = 5v + 9
• [(u(2 − 7v))/((2 − 7v))] = [(5v + 9)/((2 − 7v))]
u = [(5v + 9)/((2 − 7v))]
Solve for x:6xy + y = 3x − 2y
• 6xy + y − 3x = 3x − 2y − 3x
• 6xy + y − 3x = − 2y
• 6xy + y − 3x − y = − 2y − y
• 6xy − 3x = − 2y − y
• 6xy − 3x = − 3y
• x(6y − 3) = − 3y
• [(x(6y − 3))/((6y − 3))] = [( − 3y)/((6y − 3))]
x = [( − 3y)/((6y − 3))]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### More Than One Variable

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• More Than One Variable 0:21
• Real Life Examples
• Strategy 1:08
• Possible Techniques
• Typical Application 1:43
• Solving for a Different Variable
• Example 1: Solve for Y 5:06
• Example 2: Solve for Q 7:38
• Example 3: Solve for H 12:56
• Example 4: Solve for X 16:04