Systems of Linear Equations: math test, Grade 9 – download the PDF

1 Checking pairs / 2 pts

Consider the system \(3x + 2y = 8\) and \(x - 3y = 10\). Is \((4, -2)\) a solution? Is \((1, 5)\) a solution? Justify.

2 Solve by graphing / 3 pts

Solve the system \(y = x - 2\) and \(y = -2x + 7\) by graphing. Complete a table of values for \(x = 0, 1, 2, 3, 4\), draw both lines on a coordinate plane, and check your answer.

3 Substitution / 3 pts

Solve by substitution: \(y = -2x + 1\) and \(5x + 2y = 1\).

4 Elimination / 3 pts

Solve by elimination: \(4x + 5y = 12\) and \(6x - 7y = -40\).

5 How many solutions? / 2 pts

For each system, say how many solutions it has and explain.

1. \(y = 3x - 2\) and \(6x - 2y = 4\)
2. \(y = -x + 1\) and \(x + y = 5\)

6 Bike rental / 4 pts

Shop A charges 15 dollars plus 4 dollars per hour to rent a bike. Shop B charges 9 dollars plus 6 dollars per hour. Let \(h\) be the number of hours and \(c\) the total cost in dollars.

1. Write a system of equations.
2. After how many hours do both shops charge the same, and how much is it?
3. Which shop is cheaper for a 5-hour rental?

7 Inequalities / 3 pts

Consider the system \(x + y \le 6\) and \(y \gt 2x - 3\).

1. Which boundary line is solid and which is dashed?
2. Is \((1, 1)\) a solution? Is \((3, 2)\) a solution?
3. Find the point where the two boundary lines meet.