Solve the system
X+y=3
2x+2y=6

Infinite solutions; whenever:

x = 3 - y

Or y = 3 - x

Step-by-step explanation:

The solution of a system is, when these equations are graphed, when the lines intersect.

For linear systems, here is a summary of the number of solutions for equations:

No Solutions

When two lines are parallel, there are no solutions. Parallel lines are lines that never meet. If they never meet, there cannot be a point of intersection. In an equation, this is when the slopes are the same.

Infinite Solutions

When two lines are equivalent, there is an infinite number of solutions. This is easiest to find by converting into slope-intercept form. For some systems, you will find that multiplying or dividing the whole equation makes it equivalent. (If you try to graph an equivalent equation, you end up drawing on top of the first line.)

One Solution

All other situations, when the "m" and "b" value are not the same in slope-intercept form. Or, when the equations are not equivalent and have different slopes.

You can make 2x+2y=6 equivalent to x+y=3 .

Divide the whole equation 2x+2y=6 by 2. To do this, divide each term by two.

2x/2 + 2y/2 = 6/2

x + y = 3      <= same as the other equation

Therefore there is an infinite number of solutions.

If you need to solve for "x" and "y", you can isolate them.

Solve for "x":

x + y = 3

x + y - y = 3 - y

x = 3 - y

Solve for "y":

x + y = 3

x - x + y = 3 - x

y = 3 - x