Question

Which ordered pairs in the form (x, y) are solutions to the equation 3x – 4y = 21? Choose all answers that are correct.

A. (−3, 3)
B. (−1, −6)
C. (7, 0)
D. (11, 3)

Answer 1

The ordered pair which are solution to the equation are:

B. (-1,-6)

C. (7,0)

D. (11,3)

Explanation:

We are given a equation in terms of variables x and y as follows:

`3x-4y=21`

The ordered pair which are solutions to the equation are the points which when substituted to the equation satisfies the equation.

A)

(-3,3)

i.e. we put x= -3 and y=3 we get:

`3* (-3)-4* 3=21\\\\i.e.\\\\-9-12=21\\\\i.e.\\\\-21=21`

which is not possible.

Hence, (-3,3) is not a solution to the equation.

B)

(-1,-6)

we put x=-1 and y=-6 into the equation to get:

`3* -1-4* (-6)=21\\\\i.e.\\\\-3+24=21\\\\i.e.\\\\21=21`

Hence, (-1,-6) is a solution to the equation.

C)

(7,0)

we put x=7 and y=0 in the equation.

i.e.

`3* 7-4* 0=21\\\\i.e.\\\\21-0=21\\\\i.e.\\\\21=21`

Hence, (7,0) is a solution to the equation.

D)

(11,3)

we put x=11 and y=3 into the equation.

i.e.

`3* 11-4* 3=21\\\\i.e.\\\\33-12=21\\\\i.e.\\\\21=21`

Hence, (11,3) is a solution to the equation.

Answer 2

A. (−3, 3)
3x – 4y = 21
3(-3) - 4(3) = 21
-21 = 21 >>>>> not equal

B. (−1, −6)
3(-1) - 4(-6) = 21
21 = 21 >>>>>>>>>>Equal

C. (7, 0)
3(7) - 4(0) = 21
21 = 21>>>>>>>>>>equal

D. (11, 3)
3(11) - 4(3) = 21
21 = 21 >>>>>>>>>equal