Question

1. 7x - y = -10

-7x + y = 10

Explanation:

Step1: Observe the two equations

We have the system of equations:
$$7x - y = -10$$
$$-7x + y = 10$$

Step2: Add the two equations

If we add the left - hand sides and the right - hand sides of the two equations together:
$$(7x - y)+(-7x + y)=-10 + 10$$
Simplify the left - hand side: \(7x-7x - y + y=0\), and the right - hand side: \(0\). So we get \(0 = 0\).
This means that the two equations are actually the same line (the second equation is just the first equation multiplied by \(- 1\)). So there are infinitely many solutions, and the solutions are all the points \((x,y)\) that satisfy the equation \(7x - y=-10\) (or equivalently \(-7x + y = 10\)). We can solve for \(y\) in terms of \(x\) from the first equation: \(y=7x + 10\). So the solution set is \(\{(x,7x + 10):x\in\mathbb{R}\}\)

Answer:

The system has infinitely many solutions, and the solutions are given by \(y = 7x+10\) (or all ordered pairs \((x,y)\) such that \(7x - y=-10\)).