smart math people! i need desparate help!?

Question

Solve each system of equations by graphing and by substitution. which metod do you perfer and why?
ive been fighting with this question for hours. i dont no how to do it can someone please help me!!!!

Question:
2x + y = 5
2y = 2x + 1

Answer 1

Substitution--- because you simply solve the first eq. for y:
y=5-2x.

then everywhere you see a y in the second, you plug in (5-2x) and solve for x. Then with a value for x, plug it in the first equation, and you can solve it for y.... simple. no fractions involved, and you dont have to graph it.

Need more???

Answer 2

Either works, but in this case substitution may be easier, since you have the term 2x common to each equation.
Then 2x = 5-y (equation 1)
2x = 2y-1 (equation 2)
Subtract equation 2 from 1
5 - y = 2y - 1
Combine 6 = 3y, and y =2
Now back to the equations to solve for x.
2x = 5 - 2 and x = 3/2
Equation 2 gives the same result (hot dog)!

To graph, you want to put equations in y = mx + b format.
So y = 5 -2x (equation 1), which passes though x=0
at y=5 and has a slope of -2.

Likewise, equation 2 becomes y = x +1/2. This passes through x=0 at y=1/2 and has a slope of +1.

Answer 3

When they tell you to solve the system of equations by graphing, they want you to plug points in each equation, this will give you two seperate lines. 2x+y=5 is an equation of a line and 2y=2x+1 is also an equation of a line. Where these two lines intersect is the solution to the system. For example, 2x+y=5 when x=0, y=5. Keep putting in random values and plotting the line. And like I said where these two lines interest is the solution to the system.

Clearly that seems like a lot of work, substitution is the way to go.
For substitution, you solve an equation for a variable. Let's take 2y=2x+1 and solve for y. You get y=x+1/2. You then take this equation and plug it in the other equation you are given, you will get 2x+(x+1/2)=5, solving this equation for x, you will get x=1.5. Using x=1.5 plug it back to an original equation for x like 2x+y=5. You will get 2(1.5)+y=5. Solve this equation for y, you get y=2. So the final solution to the problem is x=1.5, y=2.

It's less time consuming to do substitution than graphing.

Hope I explained it alright. Good luck!

Answer 4

Graphing vs. Substitution: Substitution is faster, but graphing helps visual learners.

Graphing:
2x + y = 5

You need to isolate the y so...

y = -2x + 5

This graph will look like....

The y-intercept is 5 (the spot where a point hits the y, or vertical, axis) The slope is negative, so the line is pointing down to the left. The slope is 2, so for every one unit over you go 2 units down.

2y = 2x+1

Isolate the y

y = x + .5

The graph looks like...

The y-intercept is .5. The slope is positive and 1.

To find the solution, you need to find the point where those two lines intersect.


By Substitution:

2x + y = 5
y = x + .5

2x + (x+ .5) = 5

3x + .5 = 5

3x = 4.5

x = 1.5 <<<<<< this is one of your answers (the x-coordinate) (1.5, ?)

Plug the answer back in...

2(1.5) + y = 5

3 + y = 5

y = 2 <<<<< the other part of the answer (1.5, 2)

And to check:

2 (2) = 2(1.5) + 1
4= 4 << correct


Let me explain this question....

They are asking in what point the two lines (equations) intersect.

By graphing, you would be able to see visually

By substitution, you find the answer mathamatically, through calculating.

Answer 5

Well, by subsitution:
2x = 5 - y (subtracting y from both sides of eq 1)
2y = 5 - y + 1 (substitute the 2x in eq 2)
add a y:
3y = 6 (5 + 1)
y = 2

Then 2x + 2 = 5 (replace y with 2 in eq 1)
2x = 3 (substract 2 from both sides)
x = 3/2 (divide by 2)

Graphing helps you see it better, but substitution is more accurate.

Answer 6

Do your own homework. Why should we? If you are taking this class and don't know how to graph these simple equations or use the substitute method, then you weren't paying attention.