Question

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 2 and 3 comma 1 and another line that passes through the points 0 comma negative 1 and 3 comma negative 2. One solution at (−1, 0) One solution at (0, −1) Infinitely many solutions No solution

Answer 1

Answer:

no solutions (they're parallel)

Step-by-step explanation:

(0,2)(3,1)

$\frac{1-2}{3-0}$=$\frac{-1}{3}$

(0,-1)(3,-2)

$\frac{-2-(-1)}{3-0}$=$\frac{-1}{3}$

Answer 2

Answer:

No solution

Step-by-step explanation:

Solutions of a system of linear equations represented in a graph:

• Intersecting lines:  One common point = one solution.
• Parallel lines:  No common point = no solutions.
• Coincident lines:  Both equations give the same line = infinitely many solutions.

From inspection of the graph, the lines are parallel.  Therefore, there are no solutions.

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To find the solution of a system of equations given by description only, first find the slopes of the lines by substituting the given points into the slope formula.

Given points for line 1:

• (x₁, y₁) = (0, 2)
• (x₂, y₂) = (3, 1)

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-2}{3-0}=-\dfrac{1}{3}$

Given points for line 2:

• (x₁, y₁) = (0, -1)
• (x₂, y₂) = (3, -2)

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-(-1)}{3-0-x_1}=-\dfrac{1}{3}$

As the slopes of both lines are the same, the lines are parallel.

If two lines are parallel, they will never intersect and so there is no solution to the given system of equations.