How to Solve Linear Equations & Linear Inequalities
A linear equation describes a set of values in two dimensions, x and y. When this is graphed, it's a line. The equation defines what the value of the point along the y axis will be for a value of x and vice-versa. A linear inequality is much like a linear equation; it too defines a line, but that line is the demarcation of an entire region in the two-dimensional space, which may or may not include the line itself. On a graph, it appears as a whole shaded area. If the line that borders it is solid, the area of the line is included. A dotted line signals that the shaded region reaches to, but does not include, values in the line itself.
Other People Are Reading
Instructions
-
-
1
Linear equations can be mathematical statements that use addition, subtraction, multiplication or division. They have up to two variables that represent values along the x and y axes on a graph, so they are denoted as x and y. The variables cannot be multiplied or divided by each other, nor can they have exponents (powers) or roots. Examples of linear equations are: 2x + 5y = 7 and x = 9. To solve a linear equation, input values of x and solve for y. For the equation 2x + 5y = 7, an x value of 0 yields a y value of 7/5. For x = 2, y = 3/5, and so on. Since these are linear equations, finding y for only two values of x will define the line.
-
2
Plot a linear equation. Map the coordinates on a graph based on the values of x that you solved for y earlier. These were (0,7/5) and (2,3/5). Draw a line through the two points, extending beyond them. The values on this line, stretching forever in both directions, are all the values of x and y possible in the linear equation.
-
-
3
At first, linear inequalities are treated just like linear equations. So for the linear inequality 2x + 5y < 7, calculate two values for y for two inputs of x, just as before, which will yield (0,7/5) and (2,3/5) again.
-
4
Plot the border of a linear inequality. Remember that the equation states that 2x + 5y is less than 7, not equal to 7, so the values will approach the values in the line but not include them. Plot the points, but dot the line to show that it is not part of the total solution. If the expression had been 2x + 5y ≤ 7, the line would be solid because those points would be part of the solution.
-
5
Shade the appropriate region of a linear inequality. Since the expression is "less than," then the area below the line is the region that solves the equation. Shade it, as all points in that area solve the inequality.
-
1
