(-3x - 5y) = -17 and (x - 2y) = 2? Solve the system by addition.?

Answer 1

"Solve by addition" means you line up like terms between the two equations and add them to cancel out one of the variables.

However, these two equations don't have terms (e.g., 2x in one and -2x in the other) that will cancel. As a result you have to first multiply one or both of the equations to get to the point where addition will cancel out a variable.

Since you have -3x in one, let's multiply the second one (which just has x) by 3:

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

Now line it up with the other one:

3x -6y = 6
-3x -5y = -17

And add up the like terms:

3x -6y = 6
-3x -5y = -17
---- ---- = -----
0 -11y = -11

-11y = -11
y = 1

Now plug that into either equation:

x - 2y = 2
x - 2(1) = 2
x - 2 = 2
x = 4

Answer 2

Elimination by addition Method

(- 3x - 5y) = - 17- - - - - -Equation 1
(x - 2y) = 2- - - - - - - - -- Equation 2
- - - - - - - - - - - - -

Remove parenthesis equation 1 and 2

- 3x - 5y = - 17- - - -Equation 1 with out parenthesis
x - 2y = 2- - - - - - - -Equation 2 with out parenthesis
- - - - - - - - - - - -

Multiply equation 1with out parentheis by 3

x - 2y = 2

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

3x - 6y = 6

- - - - - - - - -

Elimination of x

- 3x - 5y = - 17
3x - 6y = 6
- - - - - - - - -

- 11y = - 11

- 11y / - 11 = - 11 / - 11

y = - 11 / - 11

y = 1

Insert the y value into equation 1

- - - - - - - - - - - - - - - - - -

(- 3x - 5y) = - 17

Remove parenthesis

- 3y - 5y = - 17

- 3x - 5(1) = - 17

- 3x - 5 = - 17

- 3x - 5 + 5 = - 17 + 5

- 3x = - 12

- 3x / - 3 = - 12 / - 3

x = - 12 / - 3

x = 4

Insert the x value into equation 1

- - - - - - - - - - - - - - - - - - -

Check for equation 1

(- 3x - 5y) = - 17

Remove the parenthesis

- 3x - 5y = - 17

- 3(4) - 5(1) = - 17

- 12 - 5 = - 17

- 17 = - 17

- - - - - - - - - - - -

Check for equation 2

(x - 2y = 2

Remove parenthesis

x - 2y = 2

4 - 2(1) = 2

4 - 2 = 2

2 = 2

- - - - - - - - - - -

Both equations balance

The solution set is { 1, 4 }

- - - - - - - -s-

Answer 3

Put the equations underneath each other:
-3x - 5y = -17 ... (1)
x - 2y = 2 ... (2)

Multiply the second equation by 3 so that the coefficients of x of both would be the same:

-3x - 5y = -17 ... (1)
3x - 6y = 6 ... (2)

Add the first equation to the second one. So -3x + 3x = 0; -5y + (-6y) = -5y - 6y = -11y; -17 + 6 = -11

So we are left with:
0 - 11y = -11
- 11y = -11
y = -11 divided by -11
y = 1

Substitute y=1 in one of the equations so that you could find the value of x:

-3x - 5 = -17
-3x = -17 + 5
-3x = -12
x = -12 divided by -3
x = 4

Answer 4

(-3x - 5y) = -17
(x - 2y) = 2

Multiply the second equation by 3 on each side:
(3)(x - 2y) = (3)(2)
3x - 6y = 6

Add the two equations together:
-3x - 5y = -17
3x -6y = 6
-----------------------
0x -11y = -11

-11y = -11
y = (-11 / -11) = 1

Putting this back in the first equation,
-3x -(5)(1) = -17
-3x - 5 = -17
-3x = -12
x = ( -12 / -3 ) = 4

So, x =4 and y = 1

Answer 5

-3x - 5y = -17 (*-1)
3x + 5y =17
x = (17 -5y)/3 (i)
since
x - 2y = 2
x = 2 +2y (ii)
from i and ii
2 +2y = (17 -5y)/3 (*3)
6 + 6y = 17 -5y
6+ 6y+ 5y = 17
11y = 17-6
11y = 11
y = 11/11 =1
from i x = (17 -5y)/3
then x = (17 -5*1)/3
x = 4

the answer (4 ,1)