Solve system of linear equations by the addition method?

Question

(3x + 6y = 7)
(2x + 4y = 5)

Answer 1

3x + 6y = 7- - - - - - Equation 1
2x + 4y = 5- - - - - - Equation 2
- - - - - - - - -

Multiply equation 1 by - 4 and equation 2 by 6

3x + 6y = 7

- 4(3x) + (- 4)(6y) = - 4(7)

- 12x + (- 24x) = - 28

- 12x - 24y = - 28
- - - - - -- - - - -- -

2x + 4y = 5

6(2x) + 6(4y) = 6(5)

12x + 24y = 30
- - - - - - - - - - - -

- 12x - 24y = - 28
12x + 24y = 30
- - - - - - - - - - - -
0 + 0 = 2

the coefficient and variables cancell. No solution.

- - - - - - - - - -s-

Answer 2

the first issue is to eliminate between the variables right here: upload equations a million and 2 to get 4x + 4y = 4 ==> x + y = a million ==> x = a million - y then equations a million and three 3x + 5y =7 now replace for x with the previous equation 3 - 3y + 5y = 7 ==> 2y = 4 ==> y = 2 and therefore x = -a million positioned those values for x and y into between the unique equations -a million + 6 + z = 6 ==> z = a million attempt in between the others: -3 + 2 - a million = -2 or -2 + 4 - a million = a million and also you know you've the right solutions: x = -a million y = 2 z = a million

Answer 3

Multiply the first equation by 2, and the second equation by -3:

6x + 12y = 14
-6x - 12y = -15

Add them together, and you get the equation 0 = -1. So therefore this system has no solutions (parallel lines don't intersect).