To solve a system of equations graphically, graph both equations and see where they intersect. The intersection point is the solution. The point of intersection of the two lines, is the solution to the system of equations.

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Since parallel lines never cross, then there can be no intersection; that is, for a system of equations that graphs as parallel lines, there can be no solution. This is called an “inconsistent” system of equations, and it has no solution.

The equations 3x + 2y = 6 and 3x + 2y = 12 are inconsistent. A linear system is inconsistent if it has no solution, and otherwise it is said to be consistent . When the system is inconsistent, it is possible to derive a contradiction from the equations, that may always be rewritten such as the statement 0 = 1.

**Step 1: Put the equation in Slope Intercept Form.**Step 2: Graph the y-intercept point (the number in the b position) on the y-axis. … **Step 3: From the point plotted on the y-axis, use the slope to find your second point. … **Step 4: Draw your line using the two points you plotted (y-intercept (b) first, slope (m) second.