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

Answer:

(–1, –5)

Step-by-step 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:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\ Substituting:\\y-(-8)=\frac{-2-(-8)}{0-(-2)}(x-(-2))\\y+8=3(x+2)\\y+8=3x+6\\y=3x+6-8\\y=3x-2$

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:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\ Substituting:\\y-(-9)=\frac{-5-(-9)}{-1-(-3)}(x-(-3))\\y+9=2(x+3)\\y+9=2x+6\\y=2x+6-9\\y=2x-3$

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)