Solving a System by Graphing: The Point Both Lines Share

0:00A system of linear equations is two or more equations with the same unknowns. Linear means each graph is a straight line.

0:09Ours is y equals x plus 1, and y equals negative x plus 5.

0:16A solution is an ordered pair, x and y, that makes both equations true at once.

0:23Line one crosses the y-axis at 1, its y-intercept. Its slope is 1: up 1 for each 1 to the right.

0:32Line two has y-intercept 5 and slope negative 1: down 1 for each 1 to the right.

0:40The lines cross at one point. From the grid, x is 2 and y is 3.

0:49Put x equals 2 and y equals 3 into the first equation: 3 equals 2 plus 1. True.

0:58In the second: 3 equals negative 2 plus 5. True again.

1:05The point is on both lines, so the ordered pair 2, 3 is the solution.

1:11Now take y equals x plus 1 and y equals x plus 3. Both have slope 1 but different y-intercepts, so the lines are parallel.

1:22These parallel lines never meet, so this system has no solution.

1:27Be careful when lines cross between grid lines, like y equals x plus 1 and y equals negative 2x plus 5.

1:37A rough reading gives 1.5, 2.5. It fits the first equation, but negative 2 times 1.5, plus 5, is 2, not 2.5.

1:49So that reading is wrong. The exact crossing is four thirds, seven thirds, and it checks in both.

1:58To solve a system by graphing, find where the lines cross, then check that point in both equations.