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
[tex]\begin{bmatrix}2x+y=5\\ 2x-y=55\end{bmatrix}[/tex]
subtracting
[tex]2x-y=55[/tex]
[tex]-[/tex]
[tex]\underline{2x+y=5}[/tex]
[tex]-2y=50[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}2x+y=5\\ -2y=50\end{bmatrix}[/tex]
solve -2y = 50
[tex]-2y=50[/tex]
Divide both sides by -2
[tex]\frac{-2y}{-2}=\frac{50}{-2}[/tex]
[tex]y=-25[/tex]
[tex]\mathrm{For\:}2x+y=5\mathrm{\:plug\:in\:}y=-25[/tex]
[tex]2x-25=5[/tex]
Add 25 to both sides
[tex]2x-25+25=5+25[/tex]
Simplify
[tex]2x=30[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{30}{2}[/tex]
simplify
[tex]x=15[/tex]
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.
