GMAT Quantitative Review

3.0 Math Review

3.2 Algebra

2. Equations

A major focus of algebra is to solve equations involving algebraic expressions. Some examples of such equations are

image

The solutions of an equation with one or more unknowns are those values that make the equation true, or “satisfy the equation,” when they are substituted for the unknowns of the equation. An equation may have no solution or one or more solutions. If two or more equations are to be solved together, the solutions must satisfy all the equations simultaneously.

Two equations having the same solution(s) are equivalent equations. For example, the equations

image

each have the unique solution image. Note that the second equation is the first equation multiplied by 2. Similarly, the equations

image

have the same solutions, although in this case each equation has infinitely many solutions. If any value is assigned to x, then image is a corresponding value for y that will satisfy both equations; for example, image and image is a solution to both equations, as is image and image.