Solving Systems of Linear Equations: Linear Combinations Answers

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

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

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

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

The linear combination method is applied to a system of equations as shown.4(.25x + .5y = 3.75) → x + 2y = 15 (4x – 8y = 12) → x – 2y = 3 2x = 18

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

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

Melinda and Paula shovel driveways and sidewalks in the winter as a way to earn extra money. Together they shoveled 450 square feet of sidewalk in 30 minutes. Then Melinda shoveled for 20 minutes while Paula shoveled for 25 minutes to complete 345 square feet of driveway.30x + 30y = 45020x + 25y = 345

To eliminate the x terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? First equation: Second equation:

To eliminate the y-terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together?First Equation: 5x − 4y = 28Second equation: 3x - 9y = 30