For a two-variable system of equations, there are three types of solutions: no solution, one solution, and infinitely many solutions.
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For lines which do not intersect, there is no solution.
- For lines with one point of intersection, there is one solution, which is the point of intersection.
- For lines which lie on top of each other, every point on the lines is a solution; there are infinitely many solutions.
Graph each line.
The first line has a
y-intercept of (0, 3.5) and a slope of 0.5.
The second line has a
y-intercept of (0, 0.5) and a slope of -0.5.
The solutions to a system of linear equations correspond to the points of intersection of their graphs.
The two lines on this graph intersect at the point (-3, 2).
So, the solution to the system of equations is (-3, 2), or x = -3 and y = 2.