Graph the following linear system to determine the number of solutions.

y equals negative three x plus six, six x plus two y equals twelve

0

1

2

infinitely many

Question

Graph the following linear system to determine the number of solutions.

y equals negative three x plus six, six x plus two y equals twelve

 0

 1

 2

 infinitely many

ranga · Answer

y = -3x + 6    ----- (1)
6x + 2y = 12  ----- (2)
2 is a common factor in the second equation. divide throughout by 2
3x + y = 6
y = -3x + 6

Equations (1) and (2) are one and the same.
Therefore ANY point on the first line will also be a point on the second line.
And there are INFINITE number of points on a line and each point will satisfy both equations.