Question

The data points for equation A are graphed on the coordinate plane below and are connected by using a straight line. On a coordinate plane, a line goes through (0, negative 2) and (2, 4). What is the solution to the system of equations? (–2, –8) (–1, –5) (0, –2) (2, 4)

Answer 1

the correct answer is B (–1, –5)

Answer 2

(–1, –5)

Explanation:

Two linear equations are represented by using the tables below. A 2-column table with 4 rows titled Equation A. Column 1 is labeled x with entries negative 2, 0, 3, 4. Column 2 is labeled y with entries negative 8, negative 2, 7, 10. A 2-column table with 4 rows titled Equation B. Column 1 is labeled x with entries negative 3, negative 1, 1, 5. Column 2 is labeled y with entries negative 9, negative 5, negative 1, 7. The data points for equation A are graphed on the coordinate plane below and are connected by using a straight line. On a coordinate plane, a line goes through (0, negative 2) and (2, 4). What is the solution to the system of equations? (–2, –8) (–1, –5) (0, –2) (2, 4)

Answer: To find the equation of line A, we can use any two points. Let us use points (-2, -8) and (0, -2). Therefore, the equation of line A can be gotten using the equation:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)\\ Substituting:\\y-(-8)=(-2-(-8))/(0-(-2))(x-(-2))\\y+8=3(x+2)\\y+8=3x+6\\y=3x+6-8\\y=3x-2`

To find the equation of line B, we can use any two points. Let us use points (-3, -9) and (-1, -5). Therefore, the equation of line B can be gotten using the equation:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)\\ Substituting:\\y-(-9)=(-5-(-9))/(-1-(-3))(x-(-3))\\y+9=2(x+3)\\y+9=2x+6\\y=2x+6-9\\y=2x-3`

To find the solution to the system of equations, we solve them simultaneously

y = 3x - 2 . . . 1)

y = 2x - 3 . . . 2)

Subtracting equation 2 from 1:

x + 1 = 0

x = -1

Put x = -1 in equation 1)

y = 3(-1) - 2

y = -3 - 2

y = -5

Therefore the solution to the equation is (-1, -5)