Solve the system y=2x-6; y=-1/2x+4

x = 108/5 , y = 186/5

Step-by-step explanation:

Solve the following system:

{y = 2 x - 6 | (equation 1)

y = 48 - x/2 | (equation 2)

Express the system in standard form:

{-(2 x) + y = -6 | (equation 1)

x/2 + y = 48 | (equation 2)

Add 1/4 × (equation 1) to equation 2:

{-(2 x) + y = -6 | (equation 1)

0 x+(5 y)/4 = 93/2 | (equation 2)

Multiply equation 2 by 4:

{-(2 x) + y = -6 | (equation 1)

0 x+5 y = 186 | (equation 2)

Divide equation 2 by 5:

{-(2 x) + y = -6 | (equation 1)

0 x+y = 186/5 | (equation 2)

Subtract equation 2 from equation 1:

{-(2 x)+0 y = (-216)/5 | (equation 1)

0 x+y = 186/5 | (equation 2)

Divide equation 1 by -2:

{x+0 y = 108/5 | (equation 1)

0 x+y = 186/5 | (equation 2)

Collect results:

 {x = 108/5 , y = 186/5

a) 24

b) 52ft

Step-by-step explanation:

a)

This question asks to find the capacity of the container. This is essentially asking what the volume of the container is. This can be done by multiplying the length by the width by the height.

4 * 2 * 3

= 24

b)

This question is asking how much material was used to make the prism. This is essentially asking what the surface area of the prism is. This can be found by finding the area of all the sides of the prism and then adding it up. Since it is a rectangular prism, opposite faces are congruent, hence one only has to find the area of three faces, add it up, then multiply it by two to find the answer.

2 ( 4 * 2 ) + 2 ( 3 * 4 ) + 2 ( 2 * 3 )

= 2(8) + 2(12) + 2(6)

= 16 + 24 + 12

= 52