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

Answer 1

One solution at (2, -1)

Explanation:

You will want to write the equations for both pairs of points:

(-2,-3) and (0,-2)

The slope is the change in y over the change in x. The first number of the ordered pairs is the x value and the second number in the ordered pair is the y values. Find the change by subtraction

`(-2 - -3)/(0 - -2)` =
`(-2+ 3)/(0 + 2)` =
`(1)/(2)`

The slope (m) is 1/2.

The y intercept is when x = 0. In the point (0,-2) x is 0, so the y-intercept is -2.

The y-intercept (b) is -2.

y = mx + b Substitute 1/2 for m and -2 for b

y =
`(1)/(2)`x - 2

(0,3) and (1,1)

The slope is

`(1-3)/(1-0)` =
`(-2)/(1)` = -2

The slope is --2.

The y intercept is 3.

y = mx + b Substitutes -2 for m and 3 for b.

y = -2x + 3

Set the 2 equation equal to each other and solve for x.

-2x + 3 = 1/2 x -2 Multiply all the way through by 2 to clear the fraction.

-4x + 6 = x - 4 Add 4x to both sides

-4x + 4x + 6 = x + 4x -4

6 = 5x -4 Add 4 to both sides

6 + 4 = 5x - 4 + 4

10 = 5x Divide both sides by 5

2 = x

Take either of the two original equations and substitute 2 for x and solve for y

y = -2x + 3

y = -2(2) + 3

y = -4 + 3

y = -1

The solution is (2,-1)

Helping in the name of Jesus.