SOLUTION: Determine the best method to solve each system of equations. Then solve the system. 2x+y=3x-15 x+5=4y+2x I have (18 1/3, -3 1/2) Is this correct. Thanks

Click here to see ALL problems on Equations

Question 70698: Determine the best method to solve each system of equations. Then solve the system.
2x+y=3x-15
x+5=4y+2x
I have (18 1/3, -3 1/2)
Is this correct. Thanks
Found 2 solutions by bucky, checkley75:
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
Your answer is incorrect. Maybe I can help you to find your error. Let's begin by simplifying
the two equations a little.
.
The first equation is . You have two terms that contain x. Let's move
the x from the right side by adding -3x to it. This cancels the +3x on the right side. However,
if you add -3x to the right side, you must also add -3x to the left side. When you do that
you add the -3x to the +2x that is already on the left side. The result is -x. So the first
equation is reduced to:
.

.
That's a little easier to work with. Now let's go to work on the second equation:
.

.
Notice the right side has only terms with variables. Let's move them to the left side so
the equation has all the terms containing x and y on the left side just like the first
equation does. Let's first add -2x to both sides. On the right side the -2x cancels
the +2x so the +2x disappears. And on the left side you add the -2x to the +x to get the
sum of -x. Now add -4y to the right side term of +4x. When you do the 4x is canceled and
you are left with zero on the right side. There is no y term on the left side so when we
add -4y that term appears on the left side unchanged. At this point the second equation is:
.

.
Notice now that the +5 should be on the right side instead of the left side. Move this
term to the right side by adding -5 to both sides. The -5 adds to the +5 on the left side
and it cancels it out. On the right side when we add -5 to 0 the result is -5. So finally
we are at the point of knowing that the second equation is:
.

.
Now we are at the point of saying that our set of two equations has been changed to:
.

.
To eliminate the x term we can subtract the second equation from the first equation.
(If you prefer you can think of multiplying the entire second equation by -1 and then adding
it to the first equation.) As a result of this subtraction, the x terms disappear.
The y term of the answer is 5y and the numbers on the right side subtract to give an
answer of -10. We are left with:
.

.
which we can solve by dividing both sides by 5 to get
.
Now knowing that y = -2, we can return to either of the original equations and substitute
-2 for y. Then we can solve for x. Let's return to the original first equation of:
.

.
When we substitute -2 for y in this equation, the equation becomes:
.

.
Then we can add +2 to both sides. Following that we add -3x to both sides. Do you see why?
The resulting equation is:
.

.
Since we are to solve for +x, we can do so by multiplying both sides by -1 to get:
.

.
In summary the answers are and
.
Hopefully this will help you to understand the problem and to track down your errors.

Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
2x+y=3x-15
y=3x-2x-15
y=x-15 line formula
x+5=4y+2x
4y=x-2x+5
4y=-x+5
y=-x/4+5/4 line formula
solution by graphing
(graph 300x200 pixels, x from -6 to 20, y from -20 to 20, of TWO functions y = x -15 and y = -x/4 +5/4).
solution mathematically:
y=x-15 now substitute (x-15) for y in the other formula thus:
x-15=-x/5+5/4
x+x/5=5/4+15
6x/5=5/4+60/4
6x/5=65/4 now cross multiply
6x*4=65*5
24x=325
x=325/24
x=13.54 answer now substitute 13.54 for x & solve for y.
y=13.54-15
y=-1.46 answer.