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

The first line is 1/3x and 5. For the second line the answer is (3,6).

Answer 2

1). Other line is, y =
`(1)/(3)x+5`

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

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 =
`(y_(2)-y_(1))/(x_(2)-x_(1))`

=
`(5-6)/(0-3)`

=
`(1)/(3)`

Therefore, equation of the will be,

y - 5 =
`(1)/(3)(x-0)`

y =
`(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' =
`(7-6)/(0-3)`

=
`-(1)/(3)`

Equation of the line will be,

y - 7 =
`-(1)/(3)(x-0)`

y =
`-(1)/(3)x+7` -------(2)

Therefore, equation of the other line will be, y =
`(1)/(3)x+5`

By adding equations (1) and (2),

y + y =
`-(1)/(3)x+(1)/(3)x+5+7`

2y = 12

y = 6

From equation (1),

6 =
`(1)/(3)x+5`

`(1)/(3)x=7-6`

x = 3

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