Question

How many solutions does the system have? y=3x+3 y=-2x+3

Answer 1

One solution (0, 3).

Explanation:

As both expressions in x are equal to y:

3x + 3 = -2x + 3

3x + 2x = 3 - 3

5x = 0

x =0.

So y = 3(0) + 3 = 3.

Answer 2

The system has a unique solution pair (x,y)

Explanation:

Since both linear equations are given to you solved for "y", each equation is in "slope-intercept form" which is unique. These equations show that they possess different slopes (signaled in bold in the equations below):

y = 3 x +3

y = -2 x +3

(one has slope "3" and the other one slope "-2"), and therefore they are forced to intersect. One represents a line going up (positive slope) and the other one a line going down (negative slope). That means that the system will intersect in one well defined point on the plane, giving a UNIQUE solution to the system.