Question

for the pairs below put each question in slope intercept form and whether the graphs of the line will be identical, parallel, or intersecting, Also determine how many solutions the system of equations will have​

Answer 1

3: rearrange the 2nd equation so y is isolated, add 3x to both sides
Both equations are now y = 3x + 2. So they are identical, and therefore have infinite solutions since solution means how many times do these lines meet/overlap.

4: rewrite left-right and the equations are now:
y = -x
y = -x -2
Same slope but different intercept (b value), so they are parallel and NEVER meet (NO SOLUTIONS)

5. Rearrange:
y = -x + 4
y = x + 4

So they have different SLOPES in this example (m value). This means they are not parallel or identical, so they can only cross once (one solution)

6: rearrange both
y = 3x - 1
y = 3x + 1
Same slope (m=3), different intercepts (b= 1 and -1). Same slope means parallel, different b means different intercepts so they are NOT identical. Since parallel lines can not cross, there are no solutions

7: y = 2x + 4
y = 2x - 4
Same slope (m=2), different b values (y-intercepts are 4 and -4), so parallel but not identical, no solution