Question

Select the correct answer.

What is the exact solution to the system of equations shown on the graph?

Answer 1

B. (-1 1/5, 4 3/5)

Explanation:

Answer 2

Option (B)

Explanation:

There are two lines on the graph representing the system of equations.

First line passes through two points (-3, 1) and (-2, 3).

Slope of the line =
`(y_2-y_1)/(x_2-x_1)`

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

m = 2

Equation of the line passing through (x', y') and slope = m is,

y - y' = m(x - x')

Equation of the line passing through (-3, 1) and slope = 2 will be,

y - 1 = 2(x + 3)

y = 2x + 7 ----------(1)

Second line passes through (0, 1) and (-1, 4) and y-intercept 'b' of the line is 1.

Let the equation of this line is,

y = mx + b

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

=
`(4-1)/(-1-0)`

= -3

Here 'b' = 1

Therefore, equation of the line will be,

y = -3x + 1 ---------(2)

From equation (1) and (2),

2x + 7 = -3x + 1

5x = -6

x =
`-(6)/(5)`

x =
`-1(1)/(5)`

From equation (1),

y = 2x + 7

y =
`-(12)/(5)+7`

=
`(-12+35)/(5)`

=
`(23)/(5)`

=
`4(3)/(5)`

Therefore, exact solution of the system of equations is
`(-1(1)/(5),4(3)/(5))`.

Option (B) will be the answer.