Solve simultaneous linear equations in two unknowns by algebraic methods

Follow this one with me, a step at a time. Try to guess each step first.

Worked example 1

Solve the simultaneous equations x − 2y = −11 and 4x + 4y = −8.

Remember: Make the coefficients of one unknown equal in size, then add or subtract the equations to eliminate it.

Multiply the first equation by 4 and the second equation by (−2) so that the terms in y match, then subtract: 12x = −60.
So x = −5. Substituting into the first equation gives y = 3.
Check in the first equation: 1 × (−5) + (−2) × 3 = −11.
The solution is x = −5, y = 3.

Common mistakes

This pair satisfies one equation and not the other. A solution has to satisfy both.
Swapped the values of x and y.
Made a sign slip after eliminating an unknown. Substitute into both equations to check.