Math · Equations
Systems of Linear Equations
Solve pairs of linear equations, check solutions and tell when a system has no or infinitely many solutions.
- 🎓 Grade 8
- 🧮 Math
- 📐 8.EE.C.8
- ❓ 20 questions
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Solve the system: y = 2x and x + y = 3
- A (2, 1)
- B (1, 4)
- C (1, 2)
- D (−1, −2)
Check: (1, 2) makes both equations true.
Is (1, 4) a solution of y = 3x + 1 and y = −x + 6?
- A No, only of the second
- B Yes
- C No, only of the first
- D No, of neither
−1 + 6 = 5, not 4.
The sum of two numbers is 20 and their difference is 6. What are the numbers?
- A 10 and 10
- B 12 and 8
- C 13 and 7
- D 14 and 6
Solve the system: y = 3x and x + y = −4
- A (−1, −3)
- B (0, −4)
- C (−3, −1)
- D (1, 3)
Check: (−1, −3) makes both equations true.
Solve the system: x + y = 7 and x − y = −3
- A (3, 4)
- B (5, 2)
- C (−2, −5)
- D (2, 5)
Check: (2, 5) makes both equations true.
Is (2, 3) a solution of y = x + 1 and y = 2x − 1?
- A No, of neither
- B No, only of the first
- C Yes
- D No, only of the second
Solve the system: y = 2x − 14 and 2x + y = 14
- A (8, −1)
- B (0, 7)
- C (−7, 0)
- D (7, 0)
Check: (7, 0) makes both equations true.
Solve the system: x + y = 7 and x − y = −11
- A (−2, 9)
- B (9, −2)
- C (2, −9)
- D (−1, 8)
Check: (−2, 9) makes both equations true.
Solve the system: x + y = 1 and x − y = 7
- A (4, −3)
- B (−4, 3)
- C (−3, 4)
- D (5, −4)
Check: (4, −3) makes both equations true.
On a graph, the solution of a system is shown by…
- A the point where the lines cross
- B the origin
- C the slope of each line
- D the y-intercept of each line
Adult tickets are $8 and kid tickets are $5. 10 tickets cost $62. How many adult tickets?
- A 6
- B 8
- C 4
- D 5
a + k = 10 and 8a + 5k = 62 give a = 4, k = 6.
Solve the system: y = 2x and x + y = 6
- A (2, 4)
- B (−2, −4)
- C (4, 2)
- D (3, 3)
Check: (2, 4) makes both equations true.
Solve the system: y = 2x + 7 and 2x + y = −1
- A (−2, 3)
- B (3, −2)
- C (−1, 2)
- D (2, −3)
Check: (−2, 3) makes both equations true.
Solve the system: y = 2x and x + y = −6
- A (−4, −2)
- B (−2, −4)
- C (−1, −5)
- D (2, 4)
Check: (−2, −4) makes both equations true.
Two lines have the same slope and different y-intercepts. How many solutions does the system have?
- A two
- B one
- C none
- D infinitely many
Parallel lines never meet.
Solve the system: y = 3x + 8 and 2x + y = −2
- A (−2, 4)
- B (−1, 1)
- C (−2, 2)
- D (2, −2)
Check: (−2, 2) makes both equations true.
Two lines have different slopes. How many solutions does the system have?
- A infinitely many
- B none
- C one
- D two
Two equations describe the same line. How many solutions does the system have?
- A infinitely many
- B two
- C one
- D none
Solve the system: y = 2x + 6 and 2x + y = −2
- A (−2, 4)
- B (−1, 1)
- C (2, −2)
- D (−2, 2)
Check: (−2, 2) makes both equations true.
Solve the system: x + y = 16 and x − y = −2
- A (8, 8)
- B (7, 9)
- C (−7, −9)
- D (9, 7)
Check: (7, 9) makes both equations true.
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