Extend 6-1: Graphing Technology Lab Systems of Equations
Use a graphing calculator to solve each system
of equations. Write decimal solutions to the
nearest hundredth.
1. y = 2x − 3
y = −0.4x + 5
SOLUTION: Enter these equations in the Y= list and graph. Use
the CALC menu to find the point of intersection. 2. y = 6x + 1
y = −3.2x − 4
SOLUTION: Enter these equations in the Y= list and graph. Use
the CALC menu to find the point of intersection. The solution is approximately (−0.54, −2.26)
Check the solution. The solution is approximately (3.33, 3.67) or
.
Check the answer in both equations. 3. x + y = 9.35
5x − y = 8.75
SOLUTION: Rearrange the two equations to slope-intercept form.
2. y = 6x + 1
y = −3.2x − 4
SOLUTION: Enter these equations in the Y= list and graph. Use
the CALC menu to find the point of intersection. Enter these equations in the Y= list and graph. Use
the CALC menu to find the point of intersection. The solution is approximately (−0.54, −2.26)
Check the solution. eSolutions
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Page 1
Extend 6-1: Graphing Technology Lab Systems of Equations
3. x + y = 9.35
5x − y = 8.75
SOLUTION: Rearrange the two equations to slope-intercept form.
4. 2.32x − y = 6.12
4.5x + y = −6.05
SOLUTION: Rearrange the two equations into slope-intercept
form.
Enter these equations in the Y= list and graph. Use
the CALC menu to find the point of intersection. The solution is approximately (3.02, 6.33).
Check the solution in each equation.
Enter these equations in the Y= list and graph. Use
the CALC menu to find the point of intersection. The solution is approximately (0.01, −6.10).
Check the solution in each equation.
4. 2.32x − y = 6.12
4.5x + y = −6.05
SOLUTION: Rearrange the two equations into slope-intercept
form.
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5. 5.2x − y = 4.1
1.5x + y = 6.7
SOLUTION: Rearrange the two equations into slope-intercept
form.
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Extend 6-1: Graphing Technology Lab Systems of Equations
5. 5.2x − y = 4.1
1.5x + y = 6.7
SOLUTION: Rearrange the two equations into slope-intercept
form.
6. 1.8 = 5.4x − y
y = −3.8 − 6.2x
SOLUTION: Rearrange the first equation into slope-intercept
form.
Enter these equations in the Y= list and graph. Use
the CALC menu to find the point of intersection. Enter these equations in the Y= list and graph. Use
the CALC menu to find the point of intersection. The solution is approximately (−0.17, −2.73)
The solution is approximately (1.61, 4.28).
Check the solution in each equation.
7. 7x − 2y = 16
11x + 6y = 32.3
SOLUTION: Rearrange the two equations into slope-intercept
form.
6. 1.8 = 5.4x − y
y = −3.8 − 6.2x
SOLUTION: Rearrange the first equation into slope-intercept
form.
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Enter these equations in the Y= list and graph. Use
the CALC menu to find the point of intersection.
6-1: Graphing Technology Lab Systems of Equations Extend
The solution is approximately (−0.17, −2.73)
The solution is approximately (2.51, 0.78).
7. 7x − 2y = 16
11x + 6y = 32.3
8. 3x + 2y = 16
5x + y = 9
SOLUTION: Rearrange the two equations into slope-intercept
form.
SOLUTION: Rearrange the two equations into slope-intercept
form.
Enter these equations in the Y= list and graph. Use
the CALC menu to find the point of intersection. The
solution is approximately (0.29, 7.57)
Enter these equations in the Y= list and graph. Use
the CALC menu to find the point of intersection.
9. 0.62x + 0.35y = 1.60
−1.38x + y = 8.24
SOLUTION: Rearrange the two equations into slope-intercept
form.
The solution is approximately (2.51, 0.78).
8. 3x + 2y = 16
5x + y = 9
SOLUTION: Rearrange the two equations into slope-intercept
form.
Enter these equations in the Y= list and graph. Use
the CALC menu to find the point of intersection.
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Page 4
Enter these equations in the Y= list and graph. Use
the CALC
menu to find
the point of
intersection.
Extend
6-1: Graphing
Technology
Lab
Systems ofThe
Equations solution is approximately (0.29, 7.57)
The solution is approximately (−1.16, 6.63).
9. 0.62x + 0.35y = 1.60
−1.38x + y = 8.24
SOLUTION: Rearrange the two equations into slope-intercept
form.
10. 75x − 100y = 400
33x − 10y = 70
SOLUTION: Rearrange the two equations into slope-intercept
form.
Enter these equations in the Y= list and graph. Use
the CALC menu to find the point of intersection.
Enter these equations in the Y= list and graph. Use
the CALC menu to find the point of intersection. The solution is approximately (−1.16, 6.63).
10. 75x − 100y = 400
33x − 10y = 70
SOLUTION: Rearrange the two equations into slope-intercept
form.
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The solution is approximately (1.18, −3.12).
Use a graphing calculator to solve each
equation. Write decimal solutions to the nearest
hundredth.
11. 4x − 2 = −6
SOLUTION: Write a system of equations. Set each side of the
equation equal to y. Enter these equations in the Y=
list and graph. Use the CALC menu to find the point
of intersection.
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6-1: Graphing Technology Lab Systems of Equations Extend
The solution is approximately (1.18, −3.12).
The solution is 4.
Use a graphing calculator to solve each
equation. Write decimal solutions to the nearest
hundredth.
11. 4x − 2 = −6
13. SOLUTION: Write a system of equations. Set each side of the
equation equal to y. Enter these equations in the Y=
list and graph. Use the CALC menu to find the point
of intersection.
SOLUTION: Write a system of equations. Set each side of the
equation equal to y. Enter these equations in the Y=
list and graph. Use the CALC menu to find the point
of intersection.
The solution is −2.
The solution is −1.
12. SOLUTION: Write a system of equations. Set each side of the
equation equal to y. Enter these equations in the Y=
list and graph. Use the CALC menu to find the point
of intersection. 14. SOLUTION: Write a system of equations. Set each side of the
equation equal to y. Enter these equations in the Y=
list and graph. Use the CALC menu to find the point
of intersection. The solution is 7.
The solution is 4.
13. SOLUTION: Write a system of equations. Set each side of the
equation equal to y. Enter these equations in the Y=
list and graph. Use the CALC menu to find the point
of intersection.
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15. −9 = 7 + 3x
SOLUTION: Write a system of equations. Set each side of the
equation equal to y. Enter these equations in the Y=
list and graph. Use the CALC menu to find the point
of intersection. Page 6
[–5, 5] scl: 1 by [–10, 10] scl: 1
Extend 6-1: Graphing Technology Lab Systems of Equations The solution is 7.
15. −9 = 7 + 3x
SOLUTION: Write a system of equations. Set each side of the
equation equal to y. Enter these equations in the Y=
list and graph. Use the CALC menu to find the point
of intersection. The solution is 0.5.
17. WRITING IN MATH Explain why you can solve
an equation like r = ax + b by solving the system of
equations y = r and y = ax + b.
SOLUTION: At the intersection of the graphs of y = r and y = ax
+ b, the y-values are equal. Therefore, at that point r
= ax + b.
For example, solve 3x + 3 = –2x – 7. Rewrite as y =
3x + 3 and y = –2x – 7. Solve graphically.
The solution is −5.33.
16. −2 + 10x = 8x − 1
SOLUTION: Write a system of equations. Set each side of the
equation equal to y. Enter these equations in the Y=
list and graph. Use the CALC menu to find the point
of intersection. The solution is – 1.8.
[–5, 5] scl: 1 by [–10, 10] scl: 1
The solution is 0.5.
17. WRITING IN MATH Explain why you can solve
an equation like r = ax + b by solving the system of
equations y = r and y = ax + b.
SOLUTION: At the intersection of the graphs of y = r and y = ax
+ b, the y-values are equal. Therefore, at that point r
= ax + b.
For example, solve 3x + 3 = –2x – 7. Rewrite as y =
3x + 3 and y = –2x – 7. Solve graphically.
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