We want to solve a system of linear equations, we will get that the solution is (8, -22)
A system of equations is a group of equations that we must solve simultaneously.
Here we have two lines defined by tables:
line 1:
x y
-4 26
-2 18
0 10
2 2
line 2:
x y
-4 14
-2 8
0 2
2 -4
Remember that a line is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
We know that if a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope can be computed as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
With this we can find the slope of the first line, using any pair of the given points, I will use (0, 10) and (2, 2)
[tex]a = \frac{2 - 10}{2 - 0} = -4[/tex]
And we know that the line passes through (0, 10), then the y-intercept is equal to 10.
y = -4*x + 10
For line 2 we can use the points (0, 2) and (2, - 4), so we get:
[tex]a = \frac{-4 - 2}{2 - 0} = -3[/tex]
And the y-intercept is y = 2, then the line is:
y = -3*x + 2
Now we must solve:
-4*x + 10 = -3*x + 2
10 - 2 = 4x - 3x
8 = x
Now we evaluate x = 8 in any of the two lines:
y = -3*8 + 2 = -22
Then the solution of the system is (8, -22)
If you want to learn more, you can read:
https://brainly.com/question/9351049
