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Solving Simultaneous Equations Using a Graph
(KS4, Year 10)
The Lesson
Simultaneous equations are a set of several equations with several unknowns. We can use a graph to find the values of the unknowns which solve both equations at the same time. If both equations are plotted as a line on a graph, the solution is where the lines cross.- The value of x that solves the simultaneous equations is given by the x-coordinate of the point where the lines cross.
- The value of y that solves the simultaneous equations is given by the y-coordinate of the point where the lines cross.
How to Solve Simultaneous Equations Using a Graph
Solving simultaneous equations using a graph is easy.Question
Solve the simultaneous equations shown below using a graph.Step-by-Step:
1
Plot Equation (1) on a pair of axes.
How to Plot a Linear Equation as a Line
Here is a quick way to draw a linear equation as a line:2
Plot Equation (2) on a pair of axes.
3
Find where the lines cross.
4
Read off the x-coordinate of this point.
x = 3 solves the simultaneous equations.
x = 3 solves the simultaneous equations.
5
Read off the y-coordinate of this point.
y = 2 solves the simultaneous equations.
y = 2 solves the simultaneous equations.
Answer:
We have solved the simultaneous equations:
x = 3, y = 2 solves
x + y = 5
x − y = 1
x − y = 1
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