Question

What is the solution to the following system of equations?

x − 4y = 6
2x + 2y = 12

answer choices
(0,10)
(10,0)
(6,0)
(0,6)

Answer 1

The answer to your question is (6, 0)

Explanation:

Solve the system of equations by elimination

x - 4y = 6 (I)

2x + 2y = 12 (II)

Multiply (II) by 2

x - 4y = 6

4x + 4y = 24

Simplify

5x + 0 = 30

Find x

5x = 30

x = 30/ 5

x = 6

Find "y"

6 - 4y = 6

-4y = 6 - 6

-4y = 0

y = 0/-4

y = 0

Answer 2

(6,0)

Explanation:

Given equations are:

\[x - 4y = 6\] -------------------- (1)

\[2x + 2y = 12\] -------------------- (2)

Multiplying (1) by 2 :

\[2x - 8y = 12\] -------------------- (3)

Calculating (2) - (3) :

\[2x + 2y -2x + 8y = 12 - 12\]

=> \[10y =0\]

=> \[y = 0\]

Substituting the value of y in (1):

\[ x = 6 \]

So the required solution of the system of equations is x=6,y=0. This can be alternatively expressed in coordinate notation as (6,0).