Question

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

Answer 1

Answer:

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.

Step-by-step 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

$\frac{-2y}{-2}=\frac{50}{-2}$

$y=-25$

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

$2x-25=5$

Add 25 to both sides

$2x-25+25=5+25$

Simplify

$2x=30$

Divide both sides by 2

$\frac{2x}{2}=\frac{30}{2}$

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.