Representing simultaneous equations graphically (Part 2)
Representing simultaneous equations graphically (Part 2)
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Lesson details
Key learning points
- In this lesson, we will learn to recognise simultaneous equations with no solutions by representing the equations on a graph.
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This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.
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5 Questions
Q1.
Fill in the gaps: We can use ____ to solve simultaneous equations.
Knowledge
Numbers
Terms
Q2.
What are the coordinates of the points of intersection for y = x + 5 and y = -2x - 1?
(-2, -3)
(2, -3)
(2, 3)
Q3.
Use a graph to solve y = x + 5 and y = -2x - 1 simultaneously.
x = -2, y = -3
x = 2, y = -3
x = 2, y = 3
Q4.
Create equations for the following statements: "I'm thinking of 2 numbers that have a sum of 3", "I'm thinking of 2 numbers. I triple the first number and add the second to get -1".
x + y = 3, 2x + y = -1
y = -x + 3, y = 3x - 1
y = x + 3, y = 3x - 1
Q5.
Find the values of x and y that are true for both of the following statements: "I'm thinking of 2 numbers that have a sum of 3", "I'm thinking of 2 numbers. I triple the first number and add the second to get -1".
x = -2, y = -5
x = 2, y = -5
x = 2, y = 5
5 Questions
Q1.
Which of the following statements is true?
Simultaneous equations always have solutions.
Simultaneous equations can only be solved using graphs.
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
y = x + 3, y = 2x + 3
Q3.
Which of the following equations have a solution where the x coordinate is negative?
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?
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
y = 5 - 3x, y = - 4