Answers Algebra ISolving Systems of Linear Equations: Linear Combinations

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What is the x-value of the solution to the system of equations?5x + 4y = 82x − 3y = 17

−3

−2

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Which description of the graph of the linear inequality y > 3x – 8 is correct?

The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded below the line.

The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded above the line.

The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded below the line.

The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line.

2x + 4y = 12y = x – 3

(–1, 8)

(8, –1)

(5, StartFraction one-half EndFraction)

(StartFraction one-half EndFraction, 5)

What is the y-value of the solution to the system of equations?3x + 5y = 17x + 4y = −13

−3

−1

Heather writes the equations below to represent two lines drawn on the coordinate plane.–6x + 18y = 0 4x – 12y = 20

The equation has no solution; therefore, the system of equations has no solution.

The equation has a solution at (0, 60); therefore, the system of equations has a solution at (0, 60).

The equation has infinite solutions; therefore, the system of equation as infinite solutions.

The equation has a solution at (0, 0); therefore, the system of equations has a solution at (0, 0).

What is the solution to the system of equations?y = 2x – 3.5x – 2y = –14

(–7, 3.5)

(3.5, –7)

(7, 10.5)

(10.5, 7)

y = 5x + 23x = –y + 10

(–4, –18)

(–18, –4)

(7, 1)

(1, 7)

The math team wraps gifts as a way to raise money for traveling to competitions. They offer two choices: a plain wrapping or a decorative wrapping with bows. The table represents the money raised over a busy shopping weekend.

The team charged $1 to wrap a gift with no bow and $2 to wrap a gift with a bow.

The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.

The team charged $3 to wrap a gift with no bow and $4 to wrap a gift with a bow.

The team charged $4 to wrap a gift with no bow and $5 to wrap a gift with a bow.

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, negative 1). Everything to the left of the line is shaded.

y > 2x + 3

y < 2x + 3

y > −2x + 3

y < −2x + 3

Which statements are true about the graph of the system of linear inequalities? Select two options.y > 3x – 4y < x + 1The graph of y > 3x − 4 has shading above a dashed line.The graph of y < x + 1 has shading below a dashed line.The graphs of the inequalities will intersect.There are no solutions to the system.The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).

The graph of y > 3x − 4 has shading above a dashed line.

The graph of y < x + 1 has shading below a dashed line.

The graphs of the inequalities will intersect.

There are no solutions to the system.

The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to the left of the line is shaded.

(2, 3)

(2, 1)

(3, –2)

(–1, 3)

Shawn and Dorian rented bikes from two different rental shops. The prices in dollars, y, of renting bikes from the two different shops for x hours is shown.Shop Shawn used: y=10+3.5xShop Dorian used: y=6x

Which statements about the system are true? Select two options.y = x – 43y – x = –7The system has one solution. The system consists of parallel lines.Both lines have the same slope. Both lines have the same y–intercept.The equations represent the same line.

The system has one solution.

The system consists of parallel lines.

Both lines have the same slope.

Both lines have the same y–intercept.

The equations represent the same line.

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 3) and (3, 1). Everything below and to the right of the line is shaded.

y > x – 2

y < x + 2

y > x + 1

y < x – 1

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Unit Test Answers

0 verified answers

Free Preview

What is the x-value of the solution to the system of equations?5x + 4y = 82x − 3y = 17

−3

−2

Free Preview

Which description of the graph of the linear inequality y > 3x – 8 is correct?

The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded below the line.

The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded above the line.

The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded below the line.

The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line.

2x + 4y = 12y = x – 3

(–1, 8)

(8, –1)

(5, StartFraction one-half EndFraction)

(StartFraction one-half EndFraction, 5)

What is the y-value of the solution to the system of equations?3x + 5y = 17x + 4y = −13

−3

−1

Heather writes the equations below to represent two lines drawn on the coordinate plane.–6x + 18y = 0 4x – 12y = 20

The equation has no solution; therefore, the system of equations has no solution.

The equation has a solution at (0, 60); therefore, the system of equations has a solution at (0, 60).

The equation has infinite solutions; therefore, the system of equation as infinite solutions.

The equation has a solution at (0, 0); therefore, the system of equations has a solution at (0, 0).

What is the solution to the system of equations?y = 2x – 3.5x – 2y = –14

(–7, 3.5)

(3.5, –7)

(7, 10.5)

(10.5, 7)

y = 5x + 23x = –y + 10

(–4, –18)

(–18, –4)

(7, 1)

(1, 7)

The team charged $1 to wrap a gift with no bow and $2 to wrap a gift with a bow.

The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.

The team charged $3 to wrap a gift with no bow and $4 to wrap a gift with a bow.

The team charged $4 to wrap a gift with no bow and $5 to wrap a gift with a bow.

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, negative 1). Everything to the left of the line is shaded.

y > 2x + 3

y < 2x + 3

y > −2x + 3

y < −2x + 3

The graph of y > 3x − 4 has shading above a dashed line.

The graph of y < x + 1 has shading below a dashed line.

The graphs of the inequalities will intersect.

There are no solutions to the system.

The graphs of the two inequalities intersect the y-axis at (0, 1) and (0, 4).

On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to the left of the line is shaded.

(2, 3)

(2, 1)

(3, –2)

(–1, 3)

The system has one solution.

The system consists of parallel lines.

Both lines have the same slope.

Both lines have the same y–intercept.

The equations represent the same line.

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 3) and (3, 1). Everything below and to the right of the line is shaded.

y > x – 2

y < x + 2

y > x + 1

y < x – 1

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