Solving Systems of Linear Equations: Linear Combinations

Question 1

A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75. If x is the cost of one apple and y is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange.6x+6y=7.5010x+5y=8.75

Revolt · Accepted Answer

0.5

Question 2

Which ordered pair is a solution to the system of linear equations?2x + 3y= 6–3x + 5y = 10

Revolt · Accepted Answer

(0,2)

Question 3

The system of equations shown is solved using the linear combination methodWhat does 0 = 0 mean regarding the solution to the system?

Revolt · Accepted Answer

There are infinitely many solutions to the system because the equations represent the same line.

Question 4

Mr. Brown is creating examples of systems of equations. He completes the steps to find the solution of the equation below.

Revolt · Accepted Answer

infinitely many solutions

Question 5

Karina uses the system of equations below to compare the monthly utility costs in July and December for electricity, x, and natural gas, y. 750x + 17y = 141.61300x + 30y = 75.90

Revolt · Accepted Answer

The cost of natural gas is $0.83 per unit.

Question 6

Which statement is true about the equations –3x + 4y = 12 and x – y = 1?

Revolt · Accepted Answer

The system of the equations has no solution; the two lines are parallel.

Question 7

At what value of x do the graphs of the equations below intersect?2x − y = 65x + 10y = −10

Revolt · Accepted Answer

2

Question 8

Which statement describes the graph of the system of equations below?1.5x + 0.2y = 2.681.6x + 0.3y = 2.98

Revolt · Accepted Answer

The lines intersect at (1.6,1.4).

Question 9

How many solutions are there to the system of equations?

Revolt · Accepted Answer

no solutions

Solving Systems of Linear Equations: Linear Combinations Answers

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