MATH1050: Linear Equations in Two Variables
Instructor: Laura Strube
Name
Student ID :
Answer the questions in the spaces provided or copy the questions neatly on
our own paper.
1. (5 points) Given the system:
(
4x − y = −1
5x + y = 19
(a) Find the solution to this system of equations by graphing each of the lines on the
same coordinate plane. Graph the equations on the attached graph paper, and
record the solution here.
(b) Now solve the system using substitution. Show your work and record your solution
here.
(c) What is the geometric interpretation of this solution?
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2. (5 points) Given the system:
(
−3x + y = 9
6x − 2y = −18
(a) Find the solution to this system of equations by graphing each of the lines on the
same coordinate plane. Graph the equations on the attached graph paper, and
record the solution here.
(b) Now solve the system using substitution. Show your work and record your solution
here.
(c) What is the geometric interpretation of this solution?
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3. (5 points) Given the system:
(
3x − y = 1
27x = 45 + 9y
(a) Find the solution to this system of equations by graphing each of the lines on the
same coordinate plane. Graph the equations on the attached graph paper, and
record the solution here.
(b) Now solve the system using substitution. Show your work and record your solution
here.
(c) What is the geometric interpretation of your solution?
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4. (5 points) (a) When you use substitution to solve a system of equations that describes
intersecting lines what is the result?
(b) When you use substitution to solve a system of equations that describes parallel
lines what is the result?
(c) When you use substitution to solve a system of equations that describes two identical lines what is the result?
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