A student determined that the ordered pair (1. 4) is a solution ol the following

Question

A student determined that the ordered pair (1. 4) is a solution ol the following system x+y=-3 5x + y = 3 His icasoinng was that the orderod pax satisfies the fust equation x + y = - 3, since 1 + (- 4) = - 3 What went wrong? The ordered pair (1, - 4) is not a solution of the system because the ordered pair must bo in quadrant II The ordered pair (1, - 4) is not a solution of the system because the ordered pair must be on the x axis The ordered pair (1, - 4) is not a solution of the system because the ordered pair must bo on the y-axis The ordered pair (1, - 4) is not a solution of the system because it is not a solution of the second equation

Explanation / Answer

Given : x + y = - 3...........(1)

            5x + y = 3..........(2)

ordered pair ( 1,-4)

so, by the eqn (1)

putting the ordered pair (1, -4) as x = 1 and y = -4 , we get:

1 - 4 = - 3

-3 = -3

that satisfies the equation.

now,

putting the ordered pair in eqn (2), we get:

5*(1) + (-4) = 3

5 - 4 = 3

1 = 3

that not satisfies the equation.

Hence it is clear that the point (1,-4) is the solution of x + y = - 3 but not the solution of 5x + y = 3

so, the ordered pair ( 1,-4) is not a solution of the system because it is not a solution of the second equation. Hence option (D) is the correct answer.

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