Question

determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.

$-x + y = 2$
$2x - 2y = -4$

answer attempt 1 out of 3

infinitely many solutions
one solution
no solutions

Explanation:

Step1: Simplify the second equation

Divide the second equation by 2:
$$\frac{2x - 2y}{2} = \frac{-4}{2}$$
$$x - y = -2$$

Step2: Rewrite the first equation

Multiply the first equation by -1:
$$-1\times(-x + y) = -1\times2$$
$$x - y = -2$$

Step3: Compare the two equations

Both simplified equations are identical, meaning they represent the same line, so there are infinitely many points (solutions) that satisfy both equations.

Answer:

Infinitely Many Solutions