Solving Two-Step Linear Equations
More commonly, we need two operations to solve a linear equation .
In the equation , is multiplied by and then is added. To solve two-step equations, use inverse operations to undo each operation in reverse order.
. . . . . . . our given equation
. . . . . . . . . . . . subtract from each side to get constants on the right
. . . . . . . . . . . the result
. . . . . . . .divide both sides by to isolate the
. . . . . . . . . . . . the solution (same as before!)
. . . . . . . . . . . . . . . . .We've solved the equation .
The thing that makes these equations linear is that the highest power of is (no or other powers; for those, see quadratic equations and polynomials .
Other linear equations have more than one variable: for example, . This equation has not just one but infinitely many solutions; the solutions can be graphed as a line in the plane.