From top to bottom, the answers are
- no solutions
- one solution
- infinitely many solutions
- one solution
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Step-by-step explanation:
The first system of equations has each equation with the same slope 2, but different y intercepts. This indicates we have parallel lines. Parallel lines never cross, so there are no solutions. A solution is where the two lines cross.
The second system of equation has one solution where the two lines cross. This is because the slopes are different
The third system has infinitely many solutions. We have the same line graphed out twice. One line is directly on top of the other to yield infinitely many intersection points.
The fourth system is similar to the second system. Different slopes lead to exactly one solution. The y intercept doesn't affect the number of solutions (whether its 0, 1 or infinitely many)
For each equation shown, they are in the form y = mx+b with m as the slope and b as the y intercept.