Simultaneous linear equations
Find the point that fits two equations at once: read it where the lines cross, draw the second line, eliminate a letter, meet parallel lines and get an exact answer where the graph only gives an estimate.
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Guide
Two equations with the same x and y, such as y = x + 1 and y = −2x + 4, are simultaneous equations. Each one alone has a whole line of solutions. The solution of both is the point that is on both lines: where they cross. Always give both numbers, x and y, and check them in both equations.
The elimination method: add or subtract the equations so that one letter disappears. If both have 2x, subtract them; if one has +y and the other −y, add them. Take care with the signs: subtracting −y is the same as adding y.
Parallel lines have the same gradient and never meet, however far you go, so their equations have no solution. And where lines cross between grid points, the graph only gives an estimate: work it out with algebra to get the exact answer.