Answer:
[tex] (-1\frac{1}{3}, 4\frac{3}{5}) [/tex]
Step-by-step 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 = [tex] m = \frac{rise}{run} = \frac{2}{1} = 2 [/tex]
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 = [tex] m = \frac{rise}{run} = -\frac{3}{1} = -3 [/tex]
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
[tex] x = \frac{6}{-5} = -1\frac{1}{5} [/tex]
✔️To solve for y, substitute x = -1⅕ in equation 2.
y = -3x + 1
[tex] y = -3\frac{-6}{5} + 1 [/tex]
[tex] y = \frac{18}{5} + 1 [/tex]
[tex] y = \frac{18 + 5}{5} [/tex]
[tex] y = \frac{23}{5} [/tex]
[tex] y = 4\frac{3}{5} [/tex]
✅The exact solution would be: [tex] (-1\frac{1}{3}, 4\frac{3}{5}) [/tex]
