Question

-x + 3y = 3

x - 3y = 3

Does this system have a solution?

Answer 1

No solution

Explanation:

Slope-Intercept Form: y = mx + b

Step 1: Write out systems of equations

-x + 3y = 3

x - 3y = 3

Step 2: Rewrite equations into slope-intercept form

3y = 3 + x

y = 1 + x/3

-3y = 3 - x

y = -1 + x/3

Step 3: Rewrite systems of equations

y = x/3 + 1

y = x/3 - 1

Since we have the same slope for both equations but different y-intercepts, we know that both lines are parallel. If that is the case, they will never touch or intersect each other. Therefore, we have no solution.