Geometry question help?

Question

I can't figure this out. Can someone walk me through it?

2x + 5y = 180

3x + 3y = 90

x and y have to be the same thing for both equations. Help?

Answer 1

Tom_terr is correct up to:  2x = -20 but x = -10 not -20

solution is x = -10;  y = 40

Answer 2

Actually this is geometry.  The answer is the intersecting point of two lines.

Use one equation to solve for a variable.  I'll solve for x in the second equation.  I choose the second equation because the 3's can be divided out evenly.

3x + 3y = 90

3x = 90 - 3y

x = 30 - y

Now replace the x with this in the first equation.

2x + 5y = 180

2 (30 - y) + 5y = 180  Solve for y.

60 - 2y + 5y = 180

60 + 3y = 180

3y = 180 - 60

3y = 120

y = 40

Replace 40 with y in either equation and solve for x.

3x + 3y = 90

3x + 3(40) = 90

x + 40 = 30

x = 30 - 40

x = -10

Therefore x = -10 and y = 40.  The two lines intersect at coordinate (-10, 40)

Answer 3

It's not geometry ... it's algebra.

Solve by  addition/subtraction method.

1.  multiply both equations by numbers that will allow the elimination

of either unknown.

  3 (2x + 5y)  =  3 (180)

and

  2 (3x + 3y)  =  2 (90)

gives you:

   6x + 15y  = 540

and

   6x + 6y    = 180

NOW, subtract the second one from the first one:

     9y =  360

NOW, divide by 9

      

     y = 40            - this solves for y

NOW, go back to one of the equations and replace y with 40 and solve for x.

2x  +  5y  = 180

putting in 40 gives you:

2x  + 5(40) = 180

and then

2x  + 200  = 180

NOW,  you must get the x component by itself by subtracting 200 from both sides:

  2x  + 200  -200  =  180  -200

gives

  2x =  -20

NOW, you must get the value of (1) x, by dividing both sides by 2:

  x  =  -20

Solved!

Answer 4

6x +15y =540

-15x -15y =-450

-9x =90, x= - 10

2(-10) +5y =180

5y =200, y=40