Solving Systems of Linear Equations: Graphing — Unit test Answers

Which value of m will create a system of parallel lines with no solution?y=mx-68x-4y=12

Two linear equations are shown.

A coordinate grid with 2 lines. The first line is labeled y equals 0.5 x plus 3.5 and passes through (negative 3, 1), (negative 2.7, 2.1), and (0, 3.5). The second line is labeled y equals negative StartFraction 2 over 3 EndFraction x plus StartFraction 1 over 3 EndFraction and passes through the points (negative 4, 3), (negative 2.7, 2.1), and (StartFraction 1 over 3 EndFraction, 0).

What is the solution to the system of equations?y = –5x + 3y = 1

The system of equations can be solved using linear combination to eliminate one of the variables.2x − y = −4→10x − 5y = −203x + 5y = 59→3x + 5y = 59 13x = 39Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?

What is the solution to this system of linear equations?3x – 2y = 14 5x + y = 32

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.x + y = 243x + 5y = 100What does the solution of this system indicate about the questions on the test?

What is the solution to this system of linear equations?x + y = 4x − y = 6

y=5x – 1–15x – 3y=3

What is the solution to this system of linear equations?7x – 2y = –68x + y = 3

A coordinate grid with 2 lines. The first line passes through (0, negative 5) and (negative 5, 0). The second line passes through (0, negative 5) and (negative 2, 1).

Raphael graphed the system of equations shown.y = – 3y = x – 0.8What is the best approximation for the solution to this system of equations?

What is the solution to this system of linear equations?x − 3y = −2x + 3y = 16

Which value, when placed in the box, would result in a system of equations with infinitely many solutions?y = -2x + 46x + 3y =

What is the solution to the system of equations?y = 1.5x – 4y = –x

Lian is deciding which of two gyms to join. Each gym charges a monthly rate plus a one-time membership fee.Lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. In her work, she substituted an expression for one variable and solved for the other. This resulted in the equation 75 = 75. What can Lian conclude?

Ernesto tried to determine the solution for the system of equations using substitution. His work is shown below.x – y = 73x – 2y = 8Step 1: x = y + 7Step 2: 3(y + 7) – 2y = 8Step 3: 3y + 7 – 2y = 8Step 4: y + 7 = 8Step 5: y = 1

How many solutions does this linear system have?y = 2x – 5 –8x – 4y = –20

A coordinate grid with 2 lines. The first line labeled f(x) passes through (negative 3, 3), (0, 2), and (3, 1). The second line labeled g(x) passes through the points at (negative 3, 0) and (0, 2)

A system of equations has 1 solution. If 4x – y = 5 is one of the equations, which could be the other equation?