Solving a system of equations (whos good at math)

So we have to solve the following system o equations for x and y

y=5+3x
y=30-2x

And if you could explain it too that would help! Thanks :)

If we were to graph these two lines they would either intersect at one point, intersect at all points, or not intersect at all. We know they cannot intersect at all points because they are not the same line. They must intersect because they have different slopes. At that one point that they intersect the y value and x value for both equations are the same.

Start by solving for x in one of the equations. You may choose either. I will choose the first.
y = 5+3x
3x = y - 5
x = (y-5)/3

Now plug this into the other equation. We can do this because we know at the point they intersect the x values will be equal .This will allow us to solve for the y value.

y = 30 - 2x
y = 30 - 2(y-5)/3
y = 30 - 2y/3 + 10/3
y = 100/3 - 2y/3
3y/3 = 100/3 - 2y/3

Multiply each side by 3.
3y = 100 - 2y
5y = 100
y = 20.

Now solve for the x value in either equation.
y = 5 + 3x
20 = 5 + 3x
15 = 3x
x = 5

So they intersect at (5,20)

Now lets prove that by plugging the x values into both equations and ensuring we get 20 for y.
y = 5 + 3(5) = 20 <-- OK.
y = 30 - 2(5) = 20 <-- OK.

Solved.

5+3x = 30-2x
-25 = -5x
x = 5

y = 5+3(5)
y = 20

5+3x=30-2x
5x=25
x = 5
y = 20
(5,20)

x=5