Solve Systems of Equations

The slope is the rise over the run, or the change in y over the change in x. It describes how steep or shallow the slant of a line is on a coordinate plane.

The y-intercept is the point where a line crosses the y-axis.

A linear equation is the equation of a line that increases or decreases at a constant rate. A linear equation produces a graph that is a straight line.

Let x represent the distance driven, and let y represent the amount of gas in Jenna’s tank. Then the slope of the equation is –1gal/100mi and the y-intercept is 15. This means the equation is y = [ggfrac]1/100[/ggfrac]x + 15.

All points represent solutions to the linear equation.

A system of equations is a set of equations that share all the same variables.

The substitution method is a method for solving a system of equations. In this method, one equation is set equal to a single variable and then substituted into the other equation.

The graphing method is a method for estimating the solution to a system of equations. In this method, two linear equations are graphed on the same coordinate plane. The point where the two lines intersect is the solution to the system.

No, I get the same answer no matter which variable I rearrange for, or which equation I rearrange first. There may be one variable that is easier to solve for first, in which case I may choose to solve that one first, but I don’t need to.

Yes; it is possible that a point is on one line and not the other. The solution to a system needs to be on both lines, so I need to check both equations.