How to Solve Linear Equations With Tables, Graphs and Modeling
Linear equations are equations that have a single variable that acts on a function. The idea is to isolate each side so that your unknown variable is on one side, while the solution is on the other side. When you have multiple equations in a system and their slopes are not parallel, the system is known as a consistent system and the solution to the system is where the two lines cross on a graph. By plotting points on a chart along two axes, you can determine where a system of lines crosses.
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Instructions
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Substitute "0" for the "y" value in the first equation you are given. This will give you the x intercept of that equation, or the point where the line crosses the "x" axis. For example, the "x" intercept of the equation x + y = 4 would be at the point (4,0).
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Substitute "0" for the "x" value in the first equation to get the "y" intercept of the equation. In the example above, the "y" intercept is at (0,4).
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Find a third solution to the first equation by setting the "x" value to any integer value you choose. For example, setting the "x" value to 2 would give you a solution of (2,2).
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Repeat the above steps to find the "x" intercept, "y" intercept and a third solution to the second equation you are given. For the equation y -- x = 8, the "x" intercept would be (8,0), the "y" intercept would be (0,8) and a third solution for x = 1 would be (1,9).
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Use a pencil to mark the points in the system you have been given on graph paper. It may help to use two different colors for each equation in the system to make sure there is no confusion when it comes time to draw each line.
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Use a straightedge to draw the lines to each equation in the system. If the points you have been given do not form a straight line, it is not a linear system.
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Find the point where the two lines cross. This can be accomplished by drawing lines parallel to each axis from the intersection point.
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Check the solution by substituting the values of the intersection point in both equations. The two sample equations never cross, so the system is said to have no solutions.
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References
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