KutaSoftware: Algebra 1 - System of Equations Graphing 2/2, displaying equations and plotted lines on coordinate grids.

Graphing system of equations with two linear equations on coordinate planes, showing slopes and y-intercepts for problem 5 and 6.

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- The system of equations in problem 5 is:
y = 3x - 4
y = -1/2 x + 3

The slopes are different (m₁ = 3, m₂ = -1/2), so the lines intersect at exactly one point.
Solving algebraically:
3x - 4 = -1/2 x + 3
Multiply both sides by 2: 6x - 8 = -x + 6
7x = 14 → x = 2
Substitute into first equation: y = 3(2) - 4 = 2
Solution: (2, 2)

- The system of equations in problem 6 is:
y = -2x + 2
y = -2x - 2

Both equations have the same slope (m = -2) but different y-intercepts (b₁ = 2, b₂ = -2).
This means the lines are parallel and never intersect.
Therefore, there is no solution.

Parent Tip: Review the logic above to help your child master the concept of systems of equations graphing worksheet.

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