Question

Which system of linear equations has the ordered pair (15, – 25) as its solution?

x - 2y = 35 and 2x + y = 55
x-2y = -35 and 2x - y = 55
2x+y=5 and 2x + y = 55
2x+y=5 and 2x – y=55

Answer 1

The solution to the system of equations be:

(x, y) = (15, -25)

Therefore, the fourth system of equations i.e. 2x+y=5 and 2x – y=55 has the ordered pair (15, – 25) as its solution.

Explanation:

Let us solve and check the 4th system of equations

2x+y=5

2x – y=55

solving the system of equations

`\begin{bmatrix}2x+y=5\\ 2x-y=55\end{bmatrix}`

subtracting

`2x-y=55`

`-`

`\underline{2x+y=5}`

`-2y=50`

so the system of equations becomes

`\begin{bmatrix}2x+y=5\\ -2y=50\end{bmatrix}`

solve -2y = 50

`-2y=50`

Divide both sides by -2

`(-2y)/(-2)=(50)/(-2)`

`y=-25`

`\mathrm{For\:}2x+y=5\mathrm{\:plug\:in\:}y=-25`

`2x-25=5`

Add 25 to both sides

`2x-25+25=5+25`

Simplify

`2x=30`

Divide both sides by 2

`(2x)/(2)=(30)/(2)`

simplify

`x=15`

Thus, the solution to the system of equations be:

(x, y) = (15, -25)

Therefore, the fourth system of equations i.e. 2x+y=5 and 2x – y=55 has the ordered pair (15, – 25) as its solution.