Systems of Linear Equations: Algebra 1 Math Test – PDF Download

Question 1: Is it a solution? (2 points)

Consider the system \(2x+y=7\) and \(x-3y=7\).

1. Determine whether \((4, -1)\) is a solution. (1 point)
2. Determine whether \((3, 1)\) is a solution. (1 point)

Question 2: Read the solution (2 points)

The graph shows the system \(y=-x+4\) and \(y=\frac{1}{2}x+1\).

1. State the solution of the system. (1 point)
2. Show that this solution satisfies both equations. (1 point)

Question 3: Solve by graphing (2 points)

Graph \(y=x-1\) and \(y=-2x+5\) on the grid. State the solution of the system.

Question 4: Substitution (2 points)

Solve the system \(y=4x-7\) and \(3x+2y=8\).

Question 5: Opposite coefficients (2 points)

Solve the system \(5x+3y=-1\) and \(2x-3y=-13\).

Question 6: Multiply first (2 points)

Solve the system \(3x+2y=10\) and \(5x+3y=17\).

Question 7: Count the solutions (2 points)

Determine how many solutions each system has. Justify each answer.

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

Question 8: Explain elimination (2 points)

Noah adds the equations \(3x+y=11\) and \(2x-y=4\) and gets \(5x=15\).

1. Explain why every solution of the original system must also satisfy \(5x=15\). (1 point)
2. Find the solution of the original system. (1 point)

Question 9: Ticket problem (2 points)

Sofia’s school sold 150 tickets to a concert. Student tickets cost \(\$6\) and adult tickets cost \(\$10\). Sales were $1,100. How many student tickets and how many adult tickets were sold?

Question 10: Gym memberships (2 points)

Gym A charges a \(\$30\) joining fee plus \(\$20\) per month. Gym B has no joining fee and charges \(\$35\) per month.

1. Write an equation for the total cost \(C\) after \(m\) months at each gym. (1 point)
2. Find the month when the two total costs are equal, and that cost. (1 point)

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