Substitution method math?

Question

Please help me w/ these problems, i cannot seem to solve them. You have to use the substitution method.

y=2x,
x + y=12

x=3y-1,
x + 2y=9

x + y=0,
3x + y= -4

x=3 - 3y,
x + 3y= -6

Answer 1

I'll show you how the substitution method works with the first example. You're given two equations:

y=2x,
x+y=12

Since you know that y is exactly the same as 2x, you can replace y in the second equation with 2x:

x+y = 12 becomes x+2x=12

Adding the terms gives you: 3x = 12 , and dividing both sides by 3 yields x=4.

Now, if you want to figure out y, just remember that y=2x = 2*4 = 8.
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The second example is a little more complicated, but the same exact principle applies:

x=3y-1,
x+2y=9

Replacing the x in the second equation with the 3y-1 gives you: 3y-1+2y=9 and t hen you can solve that for y.

Hope that helps!

Answer 2

In your first problem, you know that:
(1) y=2x,
(2) x + y=12


Since you are given what y is equal to, you substitute it into the second equation, like this:

x+y = 12, and you know that y = 2x, so rewrite eq (2) as

x+2x = 12, which becomes 3x = 12.

Divide both sides by three, and you have x = 4.

Now that you know the value of x, substitue it back into eq (1)

y = 2x = 2*4 = 8

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For problem 2...
(3) x=3y-1,
(4) x + 2y=9

Equation (3) gives you the value for x, substisute it into equation 4:

x + 2y = 9 becomes
3y - 1 + 2y = 9, which can be rewritten as:
5y - 1 = 9
5y = 10
y = 2

Substituting into Eq (3) you get:
x=3y-1, which becomes x = 3 *2 -1 = 5

================
(5) x + y=0,
(6) 3x + y= -4

From Eq 5, you know that x = -y
Subbing into eq 6:
3x + y = -4
3(-y) +y = -4
-3y + y = 4
-2y = 4
y = -2

Subbing back into Eq 5, you get:
x+y=0
x-2=0
x=2

================

(7) x=3 - 3y,
(8) x + 3y= -6

I cannot solve this last problem.


Hope this helps!

Answer 3

The substitution method means that you substitute the given value for a variable (for your problems, they're x or y) into a different equation. Usually, you'll want to use the value of an equation with no number, or at least the smaller number, in front of the variable. For your purposes, just use the first one in all of them. Here are at least parts of the first three.


you need to plug in the given variable for the other. For the first one, y=2x, you would have to plug in 2x for y. This means, it'd be x+2x=12. You combine those to get 3x=12. from there, x=4. then, put x into either equation. I'll use the first, since it's the easiest. y=2(4). That means y=8, giving you an answer of (4,8).

The next one, substitute (plug in) x into the 2nd equation, giving you 3y-1+2y=9.
solve that out to get the answer.

for the next one, you'd have to get just one variable on one side. I'll make it y=(negative)x. plug the new y into the second equation, then solve.

Hope this helped, and good luck. This stuff kills at first, but it becomes natural after a few problems, so don't worry too much about it.

Answer 4

Okay substitution means to substitute. So for the first one you know that y is equal to 2x so you replace the y in the second problem to 2x. So x+2x=12 then solve for x.
And you do the exact same method for the other problems. The third problem you have to minipulate the problem. So 3x + y= -4 move the 3x over to get the equation y=-3x-4. Then substitute the y in the second part of the equaiton with 3x-4. And the last one you substitute the second equaiton x with 3-3y.
Then to solve for the other variable you plug in the answer you got. I.E. for the first problem when you solve that x is 4 then you plug in 4 to get that y is equal to 8.
The answers you should have gotten are:
1)x=4 y=8
2)y=2 x=5
3)x=-2 y=2
4) unsolvable

Answer 5

In the first pair they tell you y = 2x so you will substitute that value of y into the other equation.
x + 2x = 12
3x = 12
x = 4
Now to find y substitute the value of x........y = 2(4).....y = 8
In the 2nd pair x = 3y - 1 so substitute in the other equation..
3y - 1 + 2y = 9
5y = 10
y = 2
Now to find the value of x substitute 2 for y.....x = 3(2) -1.....x = 5
The value of x and y is the solution to both equations.
In the 3rd you have to solve for x or y by subtracting so you get y = -x.....now you do the rest of your homework....