Question

One linear equation is defined by the points (2,4) and (1,1), while the other is defined by the points (2,-2) and (-1,-5). Which point represents the solutions to this system of equations?

Answer 1

Explanation:

one linear equation points: (2,4) and (1,1)

the 2nd equation points: (2,-2) and (-1,-5)

we find the equation of line of both

equation of line: y = mx + c

m = slope, c = intercept

$m\text{ = }\frac{y_2-y_1}{x_2-x_1}$

for the 1st one: (2,4) and (1,1)

m = (1-4)/(1-2) = -3/-1

m = 3

To get c, we use the slope and any point. Using point (2,4):

4 = 3(2) + c

4 = 6 + c

c = 4-6

c = -2

The equation of the line: y = 3x - 2

For the second one: