MATHEMATICS - GRAPHING SYSTEMS OF EQUATIONS

Graphing Systems Of Equations Worksheet

  • 10 questions
  • Understand that the solution of simultaneous linear equations: is the pair of values that satisfy both equations can be found algebraically (eliminating one variable) can be found graphically (point of intersection).
  • Difficulty: Medium
  • Board: CAIE
  • Attempt online on the examination portal

Here are the first 3 questions. Click “View all questions” to see the complete assessment.

Q1.

Which ordered pair is the solution of the simultaneous equations x + y = 7 and x − y = 1?

  1. A) (4,3)
  2. B) (5,2)
  3. C) (3,4)
  4. D) (2,5)

Q2.

The graphs of y = − x + 3 and y = 2x + 9 intersect at ( − 2,5). Why is this point the solution of the simultaneous equations?

  1. A) It has the same first and second coordinates.
  2. B) It is where each graph crosses the vertical axis.
  3. C) Its coordinates make both equations true.
  4. D) Its coordinates make only the first equation true.

Q3.

For the simultaneous equations 2x + y = 7 and 2x − y = 1, which step correctly eliminates one variable and finds x?

  1. A) Subtract the second equation from the first to obtain 4x = 6, so x = 1.5.
  2. B) Add the equations to obtain 4x = 8, so x = 2.
  3. C) Add the equations to obtain 4x = 6, so x = 1.5.
  4. D) Subtract the equations to obtain 2x = 8, so x = 4.

Q4.

A student claims that (3,2) is the solution of 3x + y = 11 and x − y = 1. Which statement correctly checks the claim?

  1. A) The pair satisfies only x − y = 1, so the claim is incorrect.
  2. B) The pair satisfies both equations, so the claim is correct.
  3. C) The pair satisfies only 3x + y = 11, so the claim is incorrect.
  4. D) The pair satisfies neither equation, so the claim is incorrect.

Q5.

What does a graph show about the simultaneous equations y = 3x + 2 and y = 3x − 4?

  1. A) They have the solution (0,3) because their gradients are equal.
  2. B) They have exactly one solution because their graphs intersect once.
  3. C) They have no solution because their graphs are parallel.
  4. D) They have infinitely many solutions because their graphs are the same line.

Q6.

The equations 2x + 4y = 10 and x + 2y = 5 are drawn on the same coordinate grid. Which description is correct?

  1. A) The graphs intersect once, so there is exactly one solution.
  2. B) The graphs are the same line, so there are infinitely many solutions.
  3. C) The graphs meet only at the origin, so the origin is the solution.
  4. D) The graphs are parallel, so there is no solution.

Q7.

Which step correctly eliminates y from 3x + 2y = 12 and x − 2y = 4?

  1. A) Add the equations to obtain 4x = 16.
  2. B) Add the equations to obtain 4y = 16.
  3. C) Multiply both equations to obtain 3x² − 4y² = 48.
  4. D) Subtract the second equation from the first to obtain 2x = 8.

Q8.

The figure shows the graphs of two simultaneous linear equations. What is their solution?

Diagram for question 8: The figure shows the graphs of two simultaneous linear equations. What is their solution?
  1. A) ( − 3,2)
  2. B) (3, − 2)
  3. C) (3,2)
  4. D) (2,3)

Q9.

Which labelled point in the figure represents a pair of values that satisfies both linear equations?

Diagram for question 9: Which labelled point in the figure represents a pair of values that satisfies both linear equations?
  1. A) Point C at (1, − 2)
  2. B) Point A at ( − 1,2)
  3. C) Point B at (0,3)
  4. D) Point D at ( − 2,1)

Q10.

What does the figure show about the solution of the two simultaneous linear equations?

Diagram for question 10: What does the figure show about the solution of the two simultaneous linear equations?
  1. A) The solution is (0,0) because both axes meet there.
  2. B) There is one solution because the lines intersect once.
  3. C) There are infinitely many solutions because the lines coincide.
  4. D) There is no solution because the lines do not intersect.

What this assessment covers

Concepts Tested

  • graphing systems of equations
  • Understand that the solution of simultaneous linear equations: is the pair of values that satisfy both equations can be found algebraically (eliminating one variable) can be found graphically (point of intersection).

Question Mix

  • Medium questions included

Skills you build

  • Understand

Related assessments

More practice

Other assessments in this subject