Question

Serena wants to solve the following system of equations in the most efficient way.

2 x + 3 y = 18. x + 7 y = 31.


She plans to solve for x in the first equation as her first step since both 2 and 3 can be divided into 18. Why is Serina mistaken? Serina should have solved for x in the second equation because it has a coefficient of 1. Serina should have solved for y in the first equation because dividing by 3 instead of by 2 would give a smaller number in the solution. Serina should have solved for y in the second equation because it has the largest coefficient. Serina should have solved for y in the first equation because the division step will be easier since 18 is divisible by 3.

Answer 1

A. Serina should have solved for x in the second equation because it has a coefficient of 1.

Explanation:

Serina wants to solve the following system of equations in the most efficient way.

2 x + 3 y = 18. x + 7 y = 31.

She plans to solve for x in the first equation as her first step since both 2 and 3 can be divided into 18. Why is Serina mistaken?

Serina should have solved for x in the second equation because it has a coefficient of 1.

Serina should have solved for y in the first equation because dividing by 3 instead of by 2 would give a smaller number in the solution.

Serina should have solved for y in the second equation because it has the largest coefficient.

Serina should have solved for y in the first equation because the division step will be easier since 18 is divisible by 3.

Answer 2

Serina should have solved for x in the second equation because it has a coefficient of 1.

Explanation:

we have

`2x+3y=18` ----> equation A

`x+7y=31` ---> equation B

we know that

To solve the system of equations in the most efficient way, solve for x equation B and then substitute the value of x in equation A

so

`x=31-7y` ----> equation C

substitute equation C in equation A

`2(31-7y)+3y=18`

solve for y

`62-14y+3y=18\\11y=62-18\\11y=44\\y=4`

Find the value of x

substitute the value of y in the equation C

`x=31-7(4)=3`

The solution is (3,4)

therefore

Serina should have solved for x in the second equation because it has a coefficient of 1.