Solution to an equation
I can appreciate that a solution is a value that makes the two sides of an equation balance.
- Year 8
Solution to an equation
I can appreciate that a solution is a value that makes the two sides of an equation balance.
Lesson details
Key learning points
- In an expression the variable can take any value.
- In a linear equation there is a particular value that makes the equation balance.
- The value is the solution to the linear equation.
- When graphing a linear expression this value represents a single point.
Keywords
Solution - A solution to an equality with one variable is a value which, when substituted, maintains the equality between the expressions.
Common misconception
When reading solutions from a graph pupils may read the solution as the y-coordinate.
The solution to the equation is the value of the variable that makes both sides balance.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.What is the value of the expression $$5x − 4$$ when $$x = 3$$?
Q2.What is the value of the expression $$5x − 4$$ when $$x = −1$$?
Q3.The table of values for the equation $$y = 7 − 2x$$ is shown. The missing number is .
Q4.To find the value of the expression $$21 − 1.5a$$ when $$a = 5$$, you should the variable $$a$$ for the number 5.
Q5.The graph shows 5 lines labelled A, B, C, D and E. Match each line to the equation for that line.
A (blue) - $$x = −1$$
B (pink) - $$y = x$$
C (purple) - $$y = −1$$
D (green) - $$y = 1$$
E (black) - $$y = −x$$
Q6.Match each fraction calculation to its answer.
$$4\times {1\over 2}$$ - 2
$$4\times {3\over 2}$$ - 6
$$4\times {5\over 2}$$ - 10
$$4\times {1\over 4}$$ - 1
$$4\times {3\over 4}$$ - 3
$$4\times {5\over4}$$ - 5
Assessment exit quiz
6 Questions
Q1.Which of these best describes what a solution is?
Q2.Which of these equations have a solution when $$x = 4$$?
Q3.Which of these is a solution to the equation $$3a + 5 = 2a + 2$$?
Q4.Which of these equations have no solution?
Q5.The graph shows the lines with equations $$y = 2 − 2x$$ and $$y = 2x - 2$$. What is the solution to the equation $$2x − 2 = 2 − 2x$$?
Q6.Use the graph to match each equation to its solution.
$$1 − x = 2$$ - solution when $$x = −1$$
$$1 − x = −4$$ - solution when $$x = 5$$
$$2x = 2$$ - solution when $$x = 1$$
$$2x = −4$$ - solution when $$x = −2$$
