Download Solving Systems Using Substitution

Solving Systems Using
Substitution
Substitution
• Sometimes you don’t have a graphing
calculator to use.
• Substitution allows you to solve a onevariable equation.
• One of the equations should be in either
y = or x = form – if not isolate one variable
and solve.
• Replace that variable in the other equation
and solve.
Example 1
𝑥 = 2𝑦 − 13
2𝑥 + 𝑦 = −1
• Solve 2x + y = -1 and x = 2y – 13
• Replace the x in the first equation with what x is
equal to in the second equation
• 2(2y – 13) + y = -1
• Simplify: 4y – 26 + y = -1 5y – 26 = -1
• Solve: y = 5
• Now, replace y in either equation with 5 to find x
x = 2(5) – 13
• x = -3 so the solution is (-3, 5)
• Check in the second equation 2(-3) + 5 = -1
• -6 + 5 = -1 is true so the solution is (-3, 5)
Example 2
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𝑦 = 𝑥+7
3
4𝑥 − 3𝑦 = 15
Solve: y = 4/3x – 7 and 4x – 3y = 15
Replace the y in the second equation with “3/4x – 7”
4x – 3(4/3x – 7) = 15
Simplify: 4x – 4x + 21 = 15 0x +21 = 15
Solve: 21 does not equal 15
No Solution
Example 3
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𝑦 = 𝑥+4
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𝑥 + 2𝑦 = 8
Solve: y = 1/2x + 4 and x + 2y = 8
Replace the y in the second equation with “1/2x + 4”
x + 2(1/2x + 4) = 8 Distribute
x + x + 8 = 8 Simplify
2x + 8 = 8
2x = 0
x=0
Replace the x in the first equation with 0
y = 1/2(0) + 4
y=4
(0, 4)
Check your work.
Example 4
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𝑦 = 2𝑥 + 3
𝑥 − 2𝑦 = 3
Solve:
y = 2x + 3 and x – 2y = 3
Replace y with 2x + 3 in the second equation.
x – 2(2x + 3) = 3
Distribute the –2 x – 4x – 6 = 3
Simplify
-3x – 6 = 3
Solve
-3x = 9
x = -3
Replace x with –3 in the first equation
y = 2(-3) + 3
y = -3
• So, the solution is (-3, -3) (Check it in the 2nd
equation too.)
Try these…
• x + y = 38
x = 2y – 25
• y = x + 2.8
y + 4.6 = 2x
• y=x+4
3x – 2y = -7
• x + y = 90
y = 4x - 10
• (17, 21)
• (7.4, 10.2)
• (1, 5)
• (20, 70)