Question

In the following equations, the value of x represents the price per pound of gravel and the value of y represents the price per pound of sand.2y = 3x + 85y – 15x = -30At what price for sand do the two lines intersect? (Find the value of y.)$10.00$14.00$12.33$6.67

Answer 1

$14.00

Step-by-step explanation:

2y = 3x + 8 ...(1)

5y - 15x = -30 ....(2)

To find the point of intersection, we need to solve for x and y

First let's rewrite equation (2):

divide through by 5:

y - 3x = -6

y = 3x - 6 ...(3)

Using substitution method

substitute for y in equation (1):

2(3x - 6) = 3x + 8

6x - 12 = 3x + 8

collect like terms:

6x - 3x = 8 + 12

3x = 20

x = 20/3

substitiute for x in equation 3:

y = 3(20/3) - 6

y = 20 - 6

y = 14

Since we are looking for the price per pound of sand which is the same as y.

The price for sand where the two lines intersect is $14.00