Question

. - 3x + y = 5
3x - y = - 5

Explanation:

Step1: Observe the two equations

We have the system of equations:
$$-3x + y = 5$$
$$3x - y = -5$$

Step2: Add the two equations

If we add the left - hand sides and the right - hand sides of the two equations together:
$$(-3x + y)+(3x - y)=5+(-5)$$
Simplify the left - hand side: $-3x + y+3x - y=(-3x + 3x)+(y - y)=0$
Simplify the right - hand side: $5+( - 5)=0$
We get $0 = 0$, which means the two equations are dependent (they are actually the same equation, just multiplied by - 1). So, there are infinitely many solutions. The general solution can be found by solving one of the equations for $y$. From the first equation $-3x + y = 5$, we can solve for $y$: $y=3x + 5$, where $x$ can be any real number.

Answer:

The system has infinitely many solutions, and the general solution is $y = 3x+5$ (where $x\in\mathbb{R}$)