Question

Which point of intersection is the solution to the system of equations

y=2/5x-1/2 and 1/3x+2/3

A
B
C
D

Answer 1

View the picture for the answer!

Explanation:

Answer 2

B

Explanation:

(Looking at the lines in the graph, the second equation is missing a minus sign, and should be
`y=-(1)/(3)x + (2)/(3)`)

To find the intersection point of the pair of linear equations, we just need to equate both values of y.

The equations are:

`y=(2)/(5)x - (1)/(2)`

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

Making the y from one equation equal the y of the other equation, we have:

`(2)/(5)x - (1)/(2) = -(1)/(3)x + (2)/(3)`

`(2)/(5)x +(1)/(3)x = (2)/(3) + (1)/(2)`

`(6)/(15)x +(5)/(15)x = (4)/(6) + (3)/(6)`

`(11)/(15)x = (7)/(6)`

`x = (7)/(6) * (15)/(11) =(35)/(22) = 1.591`

Then the y-coordinate of the point is found using this x-value in any of the two equations:

`y=(2)/(5)(35)/(22) - (1)/(2)`

`y=(7)/(11) - (1)/(2)`

`y=(14)/(22) - (11)/(22)`

`y=(3)/(22) = 0.136`

So the coordinate of the crossing point is (1.591, 0.136)

The point that is in this coordinate in the graph is point B.