Simultaneous equations: watch it solved step by step

Eliminate one letter, find the other, and see the two lines cross. Level: GCSE. Type any problem of this kind and the Lab works it out and animates every move, with a plain-words explanation of why.

Worked example: x + y = 10; x - y = 2

1. The pair of equations. Two equations with two unknowns, x and y. We want the one pair of numbers that makes both true at once. Method: elimination — combine the equations so one letter disappears.
2. Choose the letter to eliminate: x. The x coefficients (1 and 1) are the easiest to make match, so we will eliminate x.
3. Subtract the equations. The x terms are the same sign, so we subtract one equation from the other: the x terms cancel to leave an equation with only y.
4. Solve for y. Divide both sides by 2.
5. Substitute y = 4 into equation ①. Now we know y, put it into one of the original equations to find x.
6. Solve for x. Tidy up and solve the small equation: x = 6.
7. The solution. x = 6 and y = 4. On the graph, this is the point where the two lines cross.
8. Check in BOTH equations. Substitute x and y into both original equations. Both must come out right.

Answer: x = 6, y = 4

Practise simultaneous equations with problems the Lab marks for you.