Question

A pair of equations is shown below.

3x − y = 9
y = −2x + 11

If the two equations are graphed, at what point do the lines representing the two equations intersect?
(4, 3)
(3, 4)
(9, 11)
(11, 9)

Answer 1

3x − y = 9
y = −2x + 11

3x − (−2x + 11) = 9
3x + 2x - 11 = 9
5x = 9 + 11
5x = 20
x = 4

y = −2x + 11 = -2*4+11 = 3

(4, 3)

Answer 2

Hence, the two equations intersect at:

(4,3)

Explanation:

We are given:

A pair of equations:

3x − y = 9

y = −2x + 11

now, on graphing these equations.

as we can clearly see from the graph the two lines intersect at (4,3)

Hence, the two equations intersect at:

(4,3)