Math 8 Testlet 005 - Solving Systems of Linear Equations 8.EEI.C.8d

Ariel and Sarah are each growing a plant. The equation y = 3x + 10 can be used to model the height, y, in centimeters (cm), of Ariel’s plant after x weeks. The equation y = 4x + 3 can be used to model the height, y, in cm, of Sarah’s plant after x weeks. After how many weeks will Ariel’s and Sarah’s plants be the same height, and what will that height be?

A system of linear equations is shown.

\begin{cases} y=-\frac{1}{4}x+10\\ y=\frac{7}{4}x+2 \end{cases} What is the solution to the system of linear equations?

A system of linear equations is shown.

\begin{cases} y=-\frac{3}{2}x+1\\ y=\frac{1}{2}x+5 \end{cases} What is the solution to the system of linear equations?

A system of linear equations is shown.

\begin{cases} x=4y+14\\ 2x-3y=13 \end{cases}

Which equation shows a correct first step for solving the system of equations using

substitution?

A school sells tickets for the spring play. Adult tickets cost $9, and student tickets cost $3. The school sold 289 tickets for a total of $1,047. This situation can be represented by the system of linear equations shown.

\begin{cases} x+y=289\\ 9x+3y=1,047 \end{cases}

How many of each type of ticket did the school sell?

Two companies repair cell phones. Company A charges $25 per hour plus an initial fee of $20. Company B charges $30 per hour plus an initial fee of $10. This situation can be represented by the system of linear equations shown.

\begin{cases} y=25x+20\\ y=30x+10 \end{cases}

For which number of hours will the cost of a repair be the same with both companies?