Systems of equations

Add x + y = s and x − y = d to obtain 2x = s + d. Then x = (s + d)/2 and y = s − x. Check both equations.

In substitution, express one variable from one equation and insert that expression into the other. Solve the resulting one-variable equation, recover the other variable and check both original equations.

Add x + y = s and x − y = d to obtain 2x = s + d. Then x = (s + d)/2 and y = s − x. Check both equations.

The pair values are x and y. Calculate their sum and product separately. The pair works only when both x + y = s and xy = p hold.

From x/y = q obtain x = qy, with y ≠ 0. Substitute into the sum: (q + 1)y = s. Find y, then x = qy, and check the denominator restriction.

A system solution is a pair (x, y) satisfying both equations simultaneously. Graphically it is an intersection of their graphs. Each distinct intersection gives one pair.

Square the given x to find y. Give the solution as (x, x²), with x first.

The pair values are x and y. Calculate their sum and product separately. The pair works only when both x + y = s and xy = p hold.

If x + y = s and xy = p, both numbers are roots of t² − st + p = 0. Two distinct roots give two ordered pairs by swapping them. If x < y is required, put the smaller first; equal roots give one pair.

If x + y = s and xy = p, both numbers are roots of t² − st + p = 0. Two distinct roots give two ordered pairs by swapping them. If x < y is required, put the smaller first; equal roots give one pair.