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Back to Exercise: Solve real-world and mathematical problems leading to two linear equations in two variables

Exercises: Solving Real-World and Mathematical Problems with Systems of Linear Equations

Work through each section in order. For word problems, define your variables, write two equations, solve, and interpret your answer in a full sentence. Show your work where indicated.

Grade 8·22 problems·~30 min·Common Core Math - Grade 8·standard·8-ee-c-8c
Work through problems with immediate feedback
A

Recall / Warm-Up

1

Line pp has slope 22 and line qq has slope −3-3. Based on their slopes alone, what can you conclude about these two lines?

2

Is the pair x=4x = 4, y=1y = 1 a solution of the system x+y=5x + y = 5 and 2x−y=72x - y = 7?

3

A bag holds xx red marbles and yy blue marbles. There are 3030 marbles in all. Write the equation for the total number of marbles. Enter the number that the expression x+yx + y equals.

B

Fluency Practice

1

A concert sold aa adult tickets and ss student tickets. There were 9090 tickets sold in all, and adult tickets cost $12\text{\char"0024}12 while student tickets cost $7\text{\char"0024}7, for total sales of $880\text{\char"0024}880. Which system represents this situation?

2

Solve the system by substitution: y=x+3y = x + 3 and 2x+y=182x + y = 18. Enter the value of xx.

3

Solve the system by elimination: x+y=14x + y = 14 and x−y=2x - y = 2. Enter the value of yy.

4

Solve the system: 3x+2y=163x + 2y = 16 and x=2yx = 2y. Enter the value of xx.

5

Line 11 passes through (0,1)(0, 1) and (2,5)(2, 5). Line 22 passes through (1,0)(1, 0) and (3,4)(3, 4). Do these two lines intersect?

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