Need help solving these algebra problems. Can you help, please?

Question

Solve the following system of linear equations by the Addition Method.

2(x - 1) = 17 + 3y
-4x -7 = 3y


a. Outline the steps for solving a 2x2 system by the Additions Rule
b. Solve. Which variable did you choose to eliminate? What is the solution?

Answer 1

lets take the first linear equation and multiply through and seperate variables on the left and constants on the right.

2x - 3y = 19

Now for the other one.

-4x -3y = 7

The addition method simply means adding the two equations to solve for one variable. When you solve for one variable, you can put that number into one of the equations (which ever one you choose) and solve for the other one.

2x - 3y = 19
(+) -4x -3y = 7

Now, you have to look at the equations and see how you can elimintate one variable so that you can single out the other varible to get it's solution.

The first equation can be multiplied by (-1) so that you can eliminate the y value and solve for x. Multiplying the whole equation does not change anything and does not alter the solution.

(2x - 3y = 19) (-1)
(+) -4x -3y = 7


-2x + 3y = -19
(+)
(add terms now)

= -6x = -12

x = 2

Now, take any one of the original equations and replace x with 2.

-4x - 3y = 7 (x = 2)

-4(2) - 3y = 7

-3y = 15

y = -5

Now check your answer. Take one of the original equations and put in the values of x and y and see if it equals the value on the right of the (=) sign.

-4x - 3y = 7 ( x = 2, y = -5)

-4(2) - 3(-5) = 7

-8 +15 = 7 (works out)

There you go!

Answer 2

Can't help with the 2x2 rule .
To solve

2(x - 1) = 17 + 3y
-4x - 7 = 3y

2x - 2 = 17 + 3y
-4x - 7 = 3y

2x -3y = 19
-4x - 3y = 7 (Multiply by '-1' to eliminate 'y'

2x - 3y = 19
4x + 3y = -7
Add the two eq'ns.

6x = 12
x = 2 Substitute back into either eq'n to find 'y'.

-4x - 7 =3y
-4(2) - 7 = 3y
-8 -7 = 3y
3y = -15
y = -5

So x= 2 & y = -5 !!!! The Answer.

Answer 3

Hello

1. lets simplify everything\
2. rearrange to have standard form of x + y = number
3. then "eliminate" a variable by adding
4. plug this result back into either question to get the other variables result

2(x - 1) = 17 + 3y
-4x -7 = 3y

2x-2 = 17+3y ------- 2x-3y = 15
-4x -7 = 3y ----------- 4x+3y = -7

Now we will add the 2 equations. This will cause the "Y" to eliminate.

6x = 8
x = 4/3

Now plug back into any equation to get y = -37/9

I chose to eliminate the y since they were already opposites.

So the solution is 4/3, -37/9

Hope this helps

Answer 4

2x-2=17+3y
or 2x-3y=17+2
or 2x-3y=19------------------(1)
-4x-7=3y
or -4x-3y=7
Mutiplying with (-1),we get
4x+3y=-7-----------------------(2)
adding (1) & (2),we get
6x=12 or x=12/6=2
Putting this value in (1),we get
2*2-3y=19
or-3y=19-4=15
or y=-15/3=-5 ans

Answer 5

2x - 2 = 17 + 3y
-4x - 7 = 3y
Now multiply the 2nd equation by -1
---------------------------------------------------
2x - 2 = 17 + 3y
4x + 7 = - 3y Now add:
---------------------------------------------------
6x + 5 = 17

6x = 17 - 5
6x = 12

x = 12/6
x = 2