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

Answer:

B. (-1,-5)

Step-by-step explanation:

Line 1 (Table A):

$y-(-2)=\dfrac{-2-(-8)}{0-(-2)}\cdot (x-0)\\ \\ \\y+2=\dfrac{6}{2}\cdot x\\ \\y=3x-2$

Line 2 (Table B):

$y-(-5)=\dfrac{-9-(-5)}{-3-(-1)}\cdot (x-(-1))\\ \\ \\y+5=\dfrac{-4}{-2}\cdot (x+1)\\ \\y+5=2x+2\\ \\y=2x-3$

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)

Answer 2

Answer:

B.

Step-by-step explanation: