Question

a system of linear equations is given by the tables. one of the tables is represented by the equation y=-1/3x+7. The equation that represents the other equation is y= x + the solution of the system is ( , )

Answer 1

Answer:

1). Other line is, y = $\frac{1}{3}x+5$

2). Solution of the system is (3, 6)

Step-by-step explanation:

From the table (1),

Let the equation of the line from the given table is,

y - y' = m(x - x')

Where m = slope of the line

(x', y') is a point lying on the line.

Choose two points from the table which lie on the line.

Let the points are (0, 5) and (3, 6)

Slope = m = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

                 = $\frac{5-6}{0-3}$

                 = $\frac{1}{3}$

Therefore, equation of the will be,

y - 5 = $\frac{1}{3}(x-0)$

y = $\frac{1}{3}x+5$ -------(1)

Let the other line from the table (2) is,

y - y" = m'(x - x")

Two points taken from this table are (0, 7) and (3, 6)

m' = $\frac{7-6}{0-3}$

    = $-\frac{1}{3}$

Equation of the line will be,

y - 7 = $-\frac{1}{3}(x-0)$

y = $-\frac{1}{3}x+7$ -------(2)

Therefore, equation of the other line will be, y = $\frac{1}{3}x+5$

By adding equations (1) and (2),

y + y = $-\frac{1}{3}x+\frac{1}{3}x+5+7$

2y = 12

y = 6

From equation (1),

6 = $\frac{1}{3}x+5$

$\frac{1}{3}x=7-6$

x = 3

Therefore, solution of the system is (3, 6).