Question 6 (5 points) Which ordered pair is a solution to the following linear system?
5x + 4y= -14
x + 2y = 2
(4, -6)
(4,4)
(-6,4)
(6,4)

(-6,4)

Step-by-step explanation:

Solve the following system:

{4 y + 5 x = -14 | (equation 1)

2 y + x = 2 | (equation 2)

Subtract 1/5 × (equation 1) from equation 2:

{5 x + 4 y = -14 | (equation 1)

0 x+(6 y)/5 = 24/5 | (equation 2)

Multiply equation 2 by 5/6:

{5 x + 4 y = -14 | (equation 1)

0 x+y = 4 | (equation 2)

Subtract 4 × (equation 2) from equation 1:

{5 x+0 y = -30 | (equation 1)

0 x+y = 4 | (equation 2)

Divide equation 1 by 5:

{x+0 y = -6 | (equation 1)

0 x+y = 4 | (equation 2)

Collect results:

{x = -6 , y = 4

Step-by-step explanation:

5x + 4y = -14

-5x - 10y = - 10

-6y = -24

y=  4

x + 2(4) = 2

x + 8 = 2

x = -6

(-6, 4)

Option 3

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step-by-step explanation: