Year 9

Comparing algebraic and graphical methods for solving simultaneous equations

Year 9

Comparing algebraic and graphical methods for solving simultaneous equations

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Lesson details

Key learning points

  1. In this lesson, we will learn about the benefits of using graphical or algebraic methods to solve simultaneous equations.

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5 Questions

Q1.
Which of the following statements is true?
Simultaneous equations always have solutions.
Simultaneous equations can only be solved using graphs.
Correct answer: Simultaneous equations do not always have solutions.
Simultaneous equations never have solutions.
Q2.
Which of the following equations do not have solutions when solved simultaneously?
x + y = 2, y = x - 4
y = 2x + 1, y = -2x - 1
Correct answer: y = 3x - 2, y = 3x + 100
y = x + 3, y = 2x + 3
Q3.
Which of the following equations have a solution where the x coordinate is negative?
Correct answer: x - 2y = 6, y = -4
x - 2y = 6, y = 5 - 3x
y = 2x + 4, y = 5 - 3x
y = 5 - 3x, y = - 4
Q4.
Which of the following equations have a solution where both the coordinates are negative?
Correct answer: x - 2y = 6, y = -4
x - 2y = 6, y = 5 - 3x
y = 2x + 4, y = 5 - 3x
y = 5 - 3x, y = - 4
Q5.
Which of the following equations have a solution where both the coordinates are positive?
x - 2y = 6, y = -4
x - 2y = 6, y = 5 - 3x
Correct answer: y = 2x + 4, y = 5 - 3x
y = 5 - 3x, y = - 4

5 Questions

Q1.
Which of the following statements is true?
You can only solve simultaneous equations algebraically.
You can only solve simultaneous equations using graphs.
You can solve all simultaneous equations.
Correct answer: You can solve simultaneous equations using alegebraic and graphical methods.
Q2.
Which of the following equations can you solve simultaneously?
2y + 4x = 12 and y = -2x + 4
Correct answer: 4y + 10x = 14 and y = 2.5x + 12
y + 1 = x and y - x = 12
y = 3x + 4 and y - 3x = 12
Q3.
Solve y = 4x - 5 and 2y + 6x = 18 simultaneously using a graphical method.
y = -2, x = 3
y = 2, x = -3
y = 2, x = 3
Correct answer: y = 3, x = 2
Q4.
Solve 2y = 6x - 10 and 3y + 6x = 15 simultaneously using an algebraic method.
x = 1, y = 2
x = 2, y = -1
Correct answer: x = 2, y = 1
y = 2, x = 3
Q5.
Solve y + x = 5 and y = 5x + 11 simultaneously using both an algebraic method and a graphical method.
Correct answer: x = -1, y = 6
x = -6, y= 1
x = 1, y= - 6
x = 6, y = -1