Question

Which system of equations is equivalent to the following system?

2x + 4y = 14
4x + y = 20

A.2x + 4y = 14
-16x – 4y = -80

B.2x + 4y = 14
- 4x + y = -20

C.4x + 8y = -28
4x + y = 20

D.-2x - 4y = 14
4x + y = 20​

Answer 1

A.

Explanation:

`\left\{\begin{array}{ccc}2x+4y=14&(1)\\4x+y=20&(2)\end{array}\right\\\\\left\{\begin{array}{ccc}2x+4y=14&(1)\\4x+y=20&\text{multiply both sides by (-4)}\end{array}\right\\\left\{\begin{array}{ccc}2x+4y=14&(1)\\-16x-4y=-80&(2)\end{array}\right\to \boxed{A.}`

B.

`\left\{\begin{array}{ccc}2x+4y=14&(1)\\4x+y=20&\text{change the signs}\end{array}\right\\\\\left\{\begin{array}{ccc}2x+4y=14&(1)\\-4x-y=-20&\text{it's different to (2)}\end{array}\right`

C.

`\left\{\begin{array}{ccc}2x+4y=14&\text{multiply both sides by 2}\\4x+y=20&(2)\end{array}\right\\\left\{\begin{array}{ccc}4x+8y=28&\text{different to (1)}\\4x+y=20&(2)\end{array}\right`

D.

`\left\{\begin{array}{ccc}2x+4y=14&\text{change the signs}\\4x+y=20&(2)\end{array}\right\\\left\{\begin{array}{ccc}-2x-4y=-14&\text{different to (1)}\\4x+y=20&(2)\end{array}\right\\\\A.`

Answer 2

A

Explanation:

Given :

2x + 4y = 14 ---------- eq 1

4x + y = 20 ---------- eq 2

if you multiply eq 2 by -4 on both sides, you get

-4 (4x + y = 20) = -4 (20)

-16x -4y = -80 --------- eq3

we can see that eq. 1 and eq 2 together forms the system of equations presented in option A, Hence A is equvalent to the orginal system of equations given in the question.