Question

Select the correct answer.

What is the exact solution to the system of equations shown on the graph?
OA (-1.4)
oc (-1,63)
OD. (-1,43)

Answer 1

`(-1(1)/(3), 4(3)/(5))`

Explanation:

To find the exact solution, find the equation for each line. And solve for x and y.

To do this, represent each equation in the slope-intercept form, y = mx + b. Where m is the slope, and b is the y-intercept.

✍️Equation 1 for the line that slopes upwards from left to your right:

Slope =
`m = (rise)/(run) = (2)/(1) = 2`

b = the point at which the y-axis is intercepted by the line = 7

Substitute m = 2 and b = 7 in y = mx + b

Equation 1 would be:

✔️y = 2x + 7

✍️Equation 2 for the line that slopes downwards from left to your right:

Slope =
`m = (rise)/(run) = -(3)/(1) = -3`

b = the point at which the y-axis is intercepted by the line = 1

Substitute m = -3 and b = 1 in y = mx + b

✔️Equation 2 would be:

y = -3x + 1

✍️Solve for x and y:

✔️To solve for x, substitute y = -3x + 1 in equation 1.

y = 2x + 7

-3x + 1 = 2x + 7

Collect like terms

-3x - 2x = 7 - 1

-5x = 6

Divide both sides by -5

`x = (6)/(-5) = -1(1)/(5)`

✔️To solve for y, substitute x = -1⅕ in equation 2.

y = -3x + 1

`y = -3(-6)/(5) + 1`

`y = (18)/(5) + 1`

`y = (18 + 5)/(5)`

`y = (23)/(5)`

`y = 4(3)/(5)`

✅The exact solution would be:
`(-1(1)/(3), 4(3)/(5))`