Algebra 1 Practice Test: Solving Systems by Elimination
- Systems of Equations by Elimination
- 10 questions
- 13 minutes
These 10 questions focus on the elimination method: adding or subtracting equations so that one variable cancels. Check your answer by substituting it into both original equations.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
Solve the system: x + y = 10 and x − y = 4.
Correct answer: D
Adding the equations gives 2x = 14, so x = 7, and then y = 10 − 7 = 3. (3, 7) reverses the coordinates and fails x − y = 4.
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Question 2
Solve the system: 2x + 3y = 12 and 2x − y = 4.
Correct answer: B
Subtract the second equation from the first: 4y = 8, so y = 2. Then 2x − 2 = 4 gives x = 3. (6, 0) fits only the first equation.
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Question 3
For the system 3x + 2y = 7 and 5x − 4y = 19, which step makes the y-terms cancel when the two equations are then added?
Correct answer: A
Multiplying the first equation by 2 gives 4y, and 4y + (−4y) = 0. Multiplying by −2 gives −4y, which doubles instead of cancelling.
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Question 4
Solve the system: 3x + 2y = 7 and 5x − 4y = 19.
Correct answer: C
Double the first equation and add: 11x = 33, so x = 3. Then 9 + 2y = 7 gives y = −1. (1, 2) satisfies only the first equation.
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Question 5
Solve the system: 4x + 3y = 5 and 3x + 2y = 4.
Correct answer: D
Multiply the first equation by 2 and the second by 3: 8x + 6y = 10 and 9x + 6y = 12. Subtracting gives x = 2, then 8 + 3y = 5 gives y = −1.
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Question 6
How many solutions does the system 2x + y = 5 and 4x + 2y = 7 have?
Correct answer: B
Doubling the first equation gives 4x + 2y = 10, and subtracting the second leaves 0 = 3, which is false. The lines are parallel, so they never meet.
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Question 7
For which value of k does the system 2x + 3y = 6 and 4x + ky = 12 have infinitely many solutions?
Correct answer: C
The second equation must be exactly 2 times the first. 2(2x + 3y) = 4x + 6y = 12, so k = 6.
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Question 8
A school sold 20 tickets to a play. Adult tickets cost $8 and student tickets cost $5, and the total was $127. How many adult tickets were sold?
Correct answer: A
Use a + s = 20 and 8a + 5s = 127. Multiply the first by 5 and subtract: 3a = 27, so a = 9 and s = 11. 11 is the number of student tickets.
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Question 9
At a bakery, 3 muffins and 2 coffees cost $13.50, while 1 muffin and 2 coffees cost $8.50. What is the price of one coffee?
Correct answer: C
Subtracting the equations gives 2m = 5, so a muffin costs $2.50. Then 2.50 + 2c = 8.50 gives c = 3.00. $2.50 is the muffin price.
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Question 10
Solve the system: x2 + y = 4 and x − y = 5.
Correct answer: B
Adding the equations cancels y: 3x2 = 9, so x = 6. Then 6 − y = 5 gives y = 1. (2, 3) satisfies only the first equation.
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