Unit 3, Lesson 13
Solutions to Linear Equations
Grade 8
Student Lesson Summary
A solution to an equation with two variables is any pair of values for the variables that make the equation true. For example, the equation represents the relationship between the width and length for rectangles with a perimeter of 8 units. One solution to the equation is that the width and length could be 1 and 3, since . Another solution is that the width and length could be 2.75 and 1.25, since . There are many other possible pairs of width and length that make the equation true.
The pairs of numbers that are solutions to an equation can be seen as points on the coordinate plane where every point represents a different rectangle whose perimeter is 8 units. Here is part of the line created by all the points that are solutions to . In this situation, it makes sense for the graph to only include positive values for and since there is no such thing as a rectangle with a negative side length.
Graph of a line, origin O, with grid. Horizontal axis, scale 0 to 5, by 1’s. Vertical axis, scale 0 to 5, by 1’s. Line begins on vertical axis above origin, passes through 1 comma 3 and 2 and 75 hundredths comma 1 and 25 hundredths.
A solution to an equation with 2 variables is a pair of values for the variables that make the equation true.
For example, one solution to the equation is . Substituting 6 for and 0 for makes this equation true because .