Question

HELP ME ASAP!! Consider the graph of the system of equations. Part A: What is the system of equations that is represented by the graph shown? Part B: What is the solution to the system of equations written in Part A? Show your work.

Answer 1

Explanation:

Part (A)

From the picture attached,

Line 1 passes through two points (-2, 0) and (-1, 3).

Let the equation of the line is,

y = mx + b

where m = slope of the line

b = y-intercept

Slope of a line passing through
`(x_1,y_1)` and
`(x_2,y_2)` is given by,

m =
`(y_2-y_1)/(x_2-x_1)`

Therefore, slope of line 1,

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

m = 3

y-intercept 'b' = 6

Equation of line 1 will be,

y = 3x + 6 --------(1)

Let the equation of line 2 is,

y = m'x + b'

Since line 2 passes through two points (0, -1) and (1, 3)

Slope m' =
`(3+1)/(1-0)`

= 4

y-intercept b' = -1

Equation of line 2 is,

y = 4x - 1 --------(2)

Part (B)

By equating the values of y from both the equations,

3x + 6 = 4x - 1

4x - 3x = 6 + 1

x = 7

From equation (2),

y = 4(7) - 1

= 28 - 1

= 27