GCSE(F), GCSE(H),

Graphs can be used to estimate solutions to equations.

The solution to the equation is given where the graph crosses the *x*-axis. For some types of graphs, such as quadratics, there may be more than one solution if the line crosses the *x*-axis more than once. There may also be no solutions if the the line does not cross the *x*-axis at all.

When a solution is found, substitute back into the equation to check the answer.

1. The graph shows the function 2*x* + 3. What is the solution to 2*x* + 3 = 0?

Answer: *x* = -1.5

The line crosses the *x*-axis at - 1.5. Check the answer: 2(-1.5) + 3 = 0, which is true.

2. By drawing a graph, obtain the solution for -2*x* + 10 = 3.

Answer: *x* = 3.5

Rearrange the equation to -2*x* + 7 = 0 and plot the graph. The line crosses the *x*-axis at *x* = 3.5. Check the answer: -2(2.5) + 10 = 3, which is true.

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