Solve the system of equation by graphing : y=x+3 , 2x+y= -6 : also how do you know if it’s substitution or elimination?

Either would work, but substitution looks a bit easier.

The graph for these two is shown below.

I just put the equations in just as they are written. They did not have to be changed in any way. DESMOS is a wonderful program. Very powerful.

The blue line is 2x + y = - 6

The red line is y = x + 3

The best way to solve this other than a graph is to use substitution. Put the red graph into the blue one.

2x + y = - 6

2x +(x + 3) = - 6

2x + x + 3 = - 6

3x + 3 = - 6 Subtract 3 from both sides.

3x = - 6 - 3

3x = - 9

x = -9/3

x = -3

Now go back and solve for y

y = x + 3

y = -3 + 3

y = 0

Answer

The solution point is (-3,0) just what the graph shows.