Question

Part 1: Provide a system of TWO equations in slope-intercept form, with only one solution. Using complete sentences, explain why this system has one solution.

Part 2: Provide a system of TWO equations in slope-intercept form with no solutions. Using complete sentences, explain why this system has no solutions.

Part 3: Provide a system of TWO equations in slope-intercept form with infinitely many solutions. Using complete sentences, explain why this system has infinitely many solutions.

Answer 1

y = x +7
y = 2x +3
solve x+7 = 2x+3
4 = x
y = 4+7 =11
check
y = 2*4 +3 =11 checks
answer 4,11 is the only point where the two lines intersect

y = x+7
y = x+3
solve x+7 = x+3
7= 3 no solution
the two lines never intersect

this is the case when two equations are the same
x=y
2x = 2y
any point on the line is a solution

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Answer 2

Thanks