Question

The linear combination method is applied to a system of equations as shown. 4(.25x + .5y = 3.75) → x + 2y = 15 (4x – 8y = 12) → x – 2y = 3 2x = 18 What is the solution of the system of equations?

Answer 1

The solution of the given system is x = 9, y = 3.

Explanation:

Here, the given system of equations,

`x+2y=15--------(1)`

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

Adding equation (1) and (2),

We get,

`2x=18`

`x=9`

From equation (1),

`9+2y=15`

`2y=15-9`

`2y=6`

`y=3`

Hence, the solution of the given system is x = 9, y = 3.

Answer 2

(9, 3)

Explanation:

(1) 4(0.25x + 0.5 y) = 3.75 ⟶ x + 2y = 15

(2) 4x - 8y = 12 ⟶ x - 2y = 3

2x = 18

x = 9

9 - 2y = 3

-2y = -6

y = 3

The solution of the system of equations is (9, 3).

The graph of Equation (1) (blue) intersects that of Equation (2) (red) at (9, 3).