Substitution Problems ....S O S?

Question

I have a two problems that I must solve with Substitution, yet have no clue how to do them...

A) 2x + y = 6 B) x + 2y + 2 = 0
3x - 2y = 2 2x - 6y + 9 = 0

Answer 1

Let's take problem A first.

You have two equations:

2x + y = 6 and 3x - 2y = 2.

And, you have two variables, x and y. To solve these types of problems, you -always- need the same number of equations as there are unknowns. In this case we have two equations and two unknowns, so we can find a solution.

Arbitrarily pick one of the two equations to start with.
Lets pick 2x + y = 6.

This can be rearranged algebraically into the form
y = 6 - 2 x

So, now you know what the value of y is. It's simply 6 - 2x.

Now, take the second equation, 3x - 2y = 2

You know from the first equation that y is equal to 6 - 2x, so substitute that value into y in the second equation like this.

3x - 2y = 2
3x - 2 * (6 - 2x) = 2

You now have an equation with only one unknown, x. So, multiply it out and solve for x.

3x - 2 * (6 - 2x) = 2
3x - 12 + 4x = 2
7x - 12 = 2
7x = 14
x = 2

Now that you know the value for x, you can substitute it back into either one of the first two equations that we started with to solve for y. Pick either equation; if you didn't make a mistake you'll get the same answer either way.

Arbitrarily pick the first equation again, and substitute the value we just found for x.
2x + y = 6
2 * (2) + y = 6
4 + y = 6
y = 2

So, in this problem, both x = 2 and y = 2.

You can do the second problem. Do it exactly the same way. Express one equation in terms of one of the unknown variables.
Substitute that expression into the second equation.
Solve the second equation for the remaining variable.
Plug the value for that variable into one of two starting equations and solve for the other variable.

Hope this helps,

-Guru

Answer 2

Couldn't help but think of the song when you said this.
"S.O.S. please someone help me" - Rihanna.

2x + y = 6
3x - 2y = 2

Let's solve this by substitution. From the first equation, since
2x + y = 6, then y = -2x + 6. Plug this value of y into the second equation, to get

3x - 2y = 2
3x - 2(-2x + 6) = 2
3x + 4x - 12 = 2
7x = 14, x = 2

Therefore, y = -2x + 6 = -2(2) + 6 = -4 + 6 = 2

x = 2, y = 2 is the solution.

B)

x + 2y + 2 = 0
2x - 6y + 9 = 0

Your first step is to convert these into the form of the previous question.

x + 2y = -2
2x - 6y = -9

Solving for x in the first equation, x = -2 - 2y. Therefore

2x - 6y = -9
2[-2 - 2y] - 6y = -9
[-4 - 4y] - 6y = -9
-4 - 4y - 6y = -9
-10y = -5
y = 1/2

Therefore, x = -2 - 2y = -2 - 2(1/2) = -2 - 1 = -3

x = -3, y = 1/2

Answer 3

A) Rearrange the first equation to get y = -2x + 6 and then sub it into the second

3x - 2(-2x + 6) = 2
3x + 4x - 12 = 2
7x = 14
x = 2
Sub back in the first to get y = -2(2) + 6 = 2

Check in the second to make sure it workks:

LS = 3x - 2y = 3(2) - 2(2) = 6 - 4 = 2 = RS

Therefore the solution is (2,2).

In the second question: Isolate x in the first equation to get

x = - 2y - 2 and sub into the second equation:

2(-2y - 2) - 6y + 9 = 0
-4y - 4 - 6y + 9 = 0
-10y =-5
y = 0.5

SUb in the first to get x = -2(0.5) - 2 = -3

Check in the second to make sure it is correct:

LS = 2x - 6y + 9
= 2(-3) - 6(0.5) + 9
= -6 - 3 + 9
= 0
= RS
Therefore the solution is (-3, 0.5)

Answer 4

I am assuming that Problem A is to solve the simultaneous equations 2x+y = 6 and 3x -2y =2.. To solve the problem by subtitution you:

Step 1:
take one of the equations and solve it for one variable.
Take 2x+y = 6 and solve for x,

2x=6-y (by subtracting y from each side of the equation)
x = 3-y/2 (by dividing each side by 2)

Step 2

Substitute the value 3 - y/2 into the second equation for x.

So, 3x-2y=2 becomes 3(3-y/2) -2y =2
simplify to 9-3/2y-2y=2
9- 7/2 y=2
-7/2 y = -7 or y = 2
Step 3 Plug this value into any of the equations to get x
x = 3-y/2 x= 3-1 =2
as a test plug values into original equations to check

The second problem is solved the same way and is left to the student. :)

Answer 5

Substitution is when you solve for one variable, then substitute it in in another equal equation. For instance, in A's first equation, you can subtract 2x from both sides, which gets y = 6-2x. Substitue that into 3x-2y=2, the second equation, and you have 3x-2(6-2x)=2. Now, distribute the 2, and you have 3x-12+4x=2. Add like terms, and it simplifies further to 7x-12 = 2. Add 12 to both sides, and you find that 7x=14. Divide both sides by 7, and x is revealed as 2. Now, back to the original equation. Simplify x for 2, thnen solve for y. 2(2) + y = 6. 4+y=6. y=2. You have (2,2) as your answer. Now, check it in the second equation, just to make sure. 3(2) - 2(2) = 2, 6-4 = 2, 2=2. COrrect! You can go for the second, but if you need to check your answer, it's (-3,0.5).

Answer 6

In A) set y= 6 - 2X and the solve for x

e.g. x + 2(6 -2X) + 0
hence, x +12 - 4X = 0
3x = 12
x=4

Answer 7

no its wrong 21/3 = 7