Download March-18-2014-Answers-Full-Solutions

March 18, 2014
Pg. 357 #9-14
9.)𝟑𝒙 − 𝟏𝟎𝒚 = −𝟐𝟓
𝟒𝒙 + 𝟒𝟎𝒚 = 𝟐𝟎
STEP 1: Start with original equation given.
3𝑥 − 10𝑦 = −25
4𝑥 + 40𝑦 = 20
STEP2: Modify the equations by multiplying by a constant, which are the opposite coefficient
for the x variable of the other equation.
𝟒(3𝑥 − 10𝑦 = −25)
𝟑(4𝑥 + 40𝑦 = 20)
STEP3: Select ONE of the constants to change sign from original sign.
−4(3𝑥 − 10𝑦 = −25)
3(4𝑥 + 40𝑦 = 20)
STEP4: Distribute the constants to the equations.
−12𝑥 + 40𝑦 = 100
12𝑥 + 120𝑦 = 60
STEP5: Add the coefficients for the x and y variable and constant vertically.
0𝑥 + 160𝑦 = 160
160𝑦 = 160
STEP6: Solve for the y variable using division.
160𝑦 160
=
160
160
Solution for y variable.
𝒚=𝟏
STEP7: Re-substitute the y variable into one equation from STEP 1.
3𝑥 − 10𝑦 = −25
3𝑥 − 10(1) = −25
STEP8: Multiply
3𝑥 − 10 = −25
STEP 9: Move the constant to right side by adding or subtracting the value of the constant.
3𝑥 − 10 = −25
+10 + 10
3𝑥 = −15
STEP10: Divide by the coefficient of the variable.
3𝑥
−15
=
3
3
𝒙 = −𝟓
STEP11: Final Solution
(−𝟓, 𝟏)
10.) 𝟕𝒙 + 𝟏𝟓𝒚 = 𝟑𝟐
𝒙 − 𝟑𝒚 = 𝟐𝟎
STEP 1: Start with original equation given.
7𝑥 + 15𝑦 = 32
𝑥 − 3𝑦 = 20
STEP2: Modify the equations by multiplying by a constant, which are the opposite coefficient
for the x variable of the other equation.
𝟏(7𝑥 + 15𝑦 = 32)
𝟕(𝑥 − 3𝑦 = 20)
STEP3: Select ONE of the constants to change sign from original sign.
1(7𝑥 + 15𝑦 = 32)
−7(𝑥 − 3𝑦 = 20)
STEP4: Distribute the constants to the equations.
7𝑥 + 15𝑦 = 32
−7𝑥 + 21𝑦 = −140
STEP5: Add the coefficients for the x and y variable and constant vertically.
0𝑥 + 36𝑦 = −108
36𝑦 = −108
STEP6: Solve for the y variable using division.
36𝑦 −108
=
36
36
Solution for y variable.
𝒚 = −𝟑
STEP7: Re-substitute the y variable into one equation from STEP 1.
𝑥 − 3𝑦 = 20
𝑥 − 𝟑(−𝟑) = 20
STEP8: Multiply
𝑥 + 9 = 20
STEP 9: Move the constant to right side by adding or subtracting the value of the constant.
𝑥 + 9 = 20
−9 − 9
𝑥 = 11
STEP10: Final Solution
(𝟏𝟏, −𝟑)
𝒙 − 𝟖𝒚 = 𝟏𝟖
−𝟏𝟔𝒙 + 𝟏𝟔𝒚 = −𝟖
STEP 1: Start with original equation given.
𝑥 − 8𝑦 = 18
−16𝑥 + 16𝑦 = −8
STEP2: Modify the equations by multiplying by a constant, which are the opposite coefficient
for the x variable of the other equation.
−𝟏𝟔(𝑥 − 8𝑦 = 18)
𝟏(−16𝑥 + 16𝑦 = −8)
11.)
STEP3: Select ONE of the constants to change sign from original sign.
𝟏𝟔(𝑥 − 8𝑦 = 18)
1(−16𝑥 + 16𝑦 = −8)
STEP4: Distribute the constants to the equations.
16𝑥 − 128𝑦 = 288
−16𝑥 + 16𝑦 = −8
STEP5: Add the coefficients for the x and y variable and constant vertically.
0𝑥 + −112𝑦 = 280
−112𝑦 = 280
STEP6: Solve for the y variable using division.
−112𝑦
280
=
−112
−112
Solution for y variable.
−𝟓
𝒚 = −𝟐. 𝟓𝟎 𝒐𝒓
𝟐
STEP7: Re-substitute the y variable into one equation from STEP 1.
𝑥 − 8𝑦 = 18
𝑥 − 8(−2.5) = 18
STEP8: Multiply
𝑥 + 20 = 18
STEP 9: Move the constant to right side by adding or subtracting the value of the constant.
𝑥 + 20 = 18
−20 − 20
𝑥 = −2
STEP11: Final Solution
−𝟓
(−𝟐, −𝟐. 𝟓𝟎) 𝒐𝒓 (−𝟐,
)
𝟐
12.) 𝟐𝟒𝒙 + 𝟐𝒚 = 𝟓𝟐
𝟔𝒙 − 𝟑𝒚 = −𝟑𝟔
STEP 1: Start with original equation given.
24𝑥 + 2𝑦 = 52
6𝑥 − 3𝑦 = −36
STEP2: Modify the equations by multiplying by a constant, which are the opposite coefficient
for the x variable of the other equation.
𝟔(24𝑥 + 2𝑦 = 52)
𝟐𝟒(6𝑥 − 3𝑦 = −36)
STEP3: Select ONE of the constants to change sign from original sign.
−6(24𝑥 + 2𝑦 = 52)
24(6𝑥 − 3𝑦 = −36)
STEP4: Distribute the constants to the equations.
−144𝑥 − 𝟏𝟐𝑦 = −312
144𝑥 − 𝟕𝟐𝑦 = −864
STEP5: Add the coefficients for the x and y variable and constant vertically.
0𝑥 + −84𝑦 = −1176
−84𝑦 = −1176
STEP6: Solve for the y variable using division.
−84𝑦 −1176
=
−84
−84
Solution for y variable.
𝒚 = 𝟏𝟒
STEP7: Re-substitute the y variable into one equation from STEP 1.
6𝑥 − 3𝑦 = −36
6𝑥 − 3(14) = −36
STEP8: Multiply
6𝑥 − 42 = −36
STEP 9: Move the constant to right side by adding or subtracting the value of the constant.
6𝑥 − 42 = −36
+42 + 42
6𝑥 = 6
STEP10: Divide by the coefficient of the variable.
6𝑥
6
=
6
6
𝒙=𝟏
STEP11: Final Solution
(𝟏, 𝟏𝟒)
13.) 𝟖𝟖𝒙 − 𝟓𝒚 = 𝟑𝟗
−𝟖𝒙 + 𝟑𝒚 = −𝟏
STEP 1: Start with original equation given.
88𝑥 − 5𝑦 = 39
−8𝑥 + 3𝑦 = −1
STEP2: Modify the equations by multiplying by a constant, which are the opposite coefficient
for the x variable of the other equation.
−𝟖(88𝑥 − 5𝑦 = 39)
𝟖𝟖(−8𝑥 + 3𝑦 = −1)
STEP3: Select ONE of the constants to change sign from original sign.
𝟖(88𝑥 − 5𝑦 = 39)
88(−8𝑥 + 3𝑦 = −1)
STEP4: Distribute the constants to the equations.
704𝑥 − 40𝑦 = 312
−704𝑥 + 264𝑦 = −88
STEP5: Add the coefficients for the x and y variable and constant vertically.
0𝑥 + 224𝑦 = 224
224𝑦 = 224
STEP6: Solve for the y variable using division.
224𝑦 224
=
224
224
Solution for y variable.
𝒚=𝟏
STEP7: Re-substitute the y variable into one equation from STEP 1.
−8𝑥 + 3𝑦 = −1
−8𝑥 + 3(1) = −1
STEP8: Multiply
−8𝑥 + 3 = −1
STEP 9: Move the constant to right side by adding or subtracting the value of the constant.
−8𝑥 + 3 = −1
−3 − 3
-8𝑥 = −4
STEP10: Divide by the coefficient of the variable.
−8𝑥
−4
=
−8
−8
𝟏
𝒙 =. 𝟓 𝑶𝑹
𝟐
STEP11: Final Solution
𝟏
( , 𝟏) 𝑶𝑹 (. 𝟓, 𝟏)
𝟐
14.) 𝟐𝒙 + 𝟒𝒚 = 𝟖
𝟓𝒙 + 𝒚 = −𝟕
STEP 1: Start with original equation given.
2𝑥 + 4𝑦 = 8
5𝑥 + 𝑦 = −7
STEP2: Modify the equations by multiplying by a constant, which are the opposite coefficient
for the x variable of the other equation.
𝟓(2𝑥 + 4𝑦 = 8)
𝟐(5𝑥 + 𝑦 = −7)
STEP3: Select ONE of the constants to change sign from original sign.
−𝟓(2𝑥 + 4𝑦 = 8)
2(5𝑥 + 𝑦 = −7)
STEP4: Distribute the constants to the equations.
−10𝑥 − 20𝑦 = −40
10𝑥 + 2𝑦 = −14
STEP5: Add the coefficients for the x and y variable and constant vertically.
0𝑥 − 18𝑦 = −54
−18𝑦 = −54
STEP6: Solve for the y variable using division.
−18𝑦 −54
=
−18
−18
Solution for y variable.
𝒚=𝟑
STEP7: Re-substitute the y variable into one equation from STEP 1.
2𝑥 + 4𝑦 = 8
2𝑥 + 4(3) = 8
STEP8: Multiply
2𝑥 + 12 = 8
STEP 9: Move the constant to right side by adding or subtracting the value of the constant.
2𝑥 + 12 = 8
−12 − 12
2𝑥 = −4
STEP10: Divide by the coefficient of the variable.
2𝑥
−4
=
2
2
𝒙 = −𝟐
STEP11: Final Solution
(−𝟐, 𝟑)