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How many solutions does the system of linear equations represented in the graph have?

Coordinate plane with one line that passes through the points 0 comma 3 and 3 comma 4 and another line that passes through the points 0 comma negative 2 and 3 comma negative 1.

One solution at (−2, 0)
One solution at (0, −2)
No solution
Infinitely many solutions

Respuesta :

Answer:

I believe the answer is One solution at (0, −2)

Step-by-step explanation:

mhanifa

Answer:

  • C) No solution

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Use two points and build equation for each line.

Slope - intercept form is:

  • y = mx + b, where m- slope, b - y-intercept

Line 1

Points:

  • (0, 3) and (3, 4)

We see b = 3, finding the slope:

  • m = (4 - 3)/(3 - 0) = 1/3

The line is:

  • y = (1/3)x + 3

Line 2

Points:

  • (0, -2) and (3, - 1)

We see b = -2, finding the slope:

  • m = (-1 + 2)/(3 - 0) = 1/3

The line is:

  • y = (1/3)x - 2

Comparing the lines, we see they have same slopes but different y-intercepts. It means the lines are parallel. Since parallel lines don't intersect, there is no solution.

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