Question

Two linear equations are represented by using the tables below.

EQUATION A TABLE-
(-2,-8) (0,-2) (3,7) (4,10)
EQUATION B TABLE-
(-3,-9) (-1,-5) (1,-1) (5,7)

The data points for equation A are graphed on the coordinate plane below and are connected by using a straight line.

What is the solution to the system of equations?

A. (-2, -8)
B. (-1, -5)
C. (0, -2)
D. (2, 4)
PLEASE EXPLAIN THE ANSWER

Answer 1

B. (-1,-5)

Explanation:

Line 1 (Table A):

`y-(-2)=(-2-(-8))/(0-(-2))\cdot (x-0)\\ \\ \\y+2=(6)/(2)\cdot x\\ \\y=3x-2`

Line 2 (Table B):

`y-(-5)=(-9-(-5))/(-3-(-1))\cdot (x-(-1))\\ \\ \\y+5=(-4)/(-2)\cdot (x+1)\\ \\y+5=2x+2\\ \\y=2x-3`

Equate these two equations:

`3x-2=2x-3\\ \\3x-2x=-3+2\\ \\x=-1`

Substitute it into the first equation:

`y=3\cdot (-1)-2=-3-2=-5`

The solution to the system of equations is (-1,-5)