Question

A system of linear equations includes the line that is created by the equation y=0.5x-1 and the line through the points (3, 1) and (–5, –7), shown below.

What is the solution to the system of equations?

a. (–6, –4)
b. (0, –1)
c. (0, –2)
d. (2, 0)

Answer 1

The answer is (2,0). If you graph the lines, it shows that the intersection occurs right there.

Answer 2

Answer: Solution is,

d. (2, 0)

Explanation:

Since, the equation of line that passes through points
`(x_1,y_1)` and
`(x_2,y_2)` is,

`(y-y_1)=(x_2-x_1)/(y_2-y_1)(y-y_1)`

Thus, the equation of line through the points (3, 1) and (–5, –7) is,

`(y-1)=(-7-1)/(-5-3)(x-3)`

`(y-1)=(-8)/(-8)(x-3)`

`y - 1 = x - 3`

`\implies y = x - 2------(1)`,

Equation of second line is,

`y = 0.5x - 1 -----(2)`,

By equation (1) and (2),

x - 2 = 0.5x - 1 ⇒ 0.5x = 1 ⇒ x = 2,

From equation (1),

We get, y = 0,

Hence, the solution of line (1) and (2) is (2,0).