Simultaneous linear equations

Find values satisfying two linear conditions and check with equations and graphs.

Meaning

A system's solution is a set of values making every equation true at once. Substitution and elimination combine conditions to reduce the unknowns.

Example

Adding and gives so The ordered pair satisfies both.The y coefficients are 1 and −1, so addition eliminates y. Keep an original equation as well: the sum alone loses information. Recover y and check both originals. Alternatively, substitute y=11−x from the first into the second to express the same y in terms of x.Satisfying only one equation is insufficient. Two lines can meet at one point, be parallel, or coincide.

Practice for this concept

Scope and references

Topics

Satisfying two conditions, substitution, elimination, solutions and graphs

Learning goal

Find values satisfying two linear conditions and check with equations and graphs.

Helpful background

Explore each equation's solutions and simultaneous satisfaction.