IGCSE Maths / Simultaneous equations
Simultaneous equations from a graph
Edexcel International GCSE Maths (4MA1), chapter 7: Simultaneous equations, specification point 2.6b. Free lesson.
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A pair of simultaneous equations is true for the same values of x and y. On a graph, its solution is the point where the two lines cross, so you must read the coordinates in the order x first, then y.
What the point of intersection means
The point of intersection is where two lines meet. Its coordinates give the one pair of values that fits both equations at once. When asked to solve, write the values separately as x = and y =, rather than giving only a coordinate.
How to find where two lines cross
To plot an equation, first write it in the form y = mx + c. You can then work out a few points for each line. A point where both equations give the same y-value for the same x-value is their intersection.
How to read the answer from the graph
On a graph, x is the distance across and y is the distance up. Read the crossing point across first, then up. For the lines y = 2x − 1 and x + y = 5, the shared point is (2, 3), so write x = 2 and y = 3.
When the question says “on the grid”
The wording tells you which method to use. If it says to solve the equations on the grid, draw both lines and mark where they cross. An answer found by algebra alone, with no lines drawn, does not earn the marks for the graph method. Draw both lines. Mark their crossing point. Write the answer as x = and y =.
Check the coordinate order
Coordinates are written (x, y), so the first number is how far across and the second is how far up. If the point is (2, 3), writing x = 3 and y = 2 swaps the values and gives the wrong answer.