Question

For which system of equations is (2, 2) a solution?

a. –3x + 3y = 0 x + 6y = 10
b. –2x + 5y = –6 4x – 2y = 4
c. 5x – 2y = –6 3x – 4y = 2
d. 2x + 3y = 10 4x + 5y = 18

Answer 1

Plug the values (x,y)=(2,2) into the equations and check if they satsify them.

a.

`-3x+3y=0 \\ x+6y=10 \\ \\ \hbox{the first equation:} \\ -3 * 2+3 * 2=0 \\ -6+6=0 \\ 0=0 \\ true \\ \\ \hbox{the second equation:} \\ 2+6 * 2=10 \\ 2+12=10 \\ 14=10 \\ false \\ \\ \hbox{(2,2) satisfies only one of the equations} \\ \hbox{so it's not a solution to the system of equations}`

b.

`-2x+5y=-6 \\ 4x-2y=4 \\ \\ \hbox{the first equation:} \\ -2 * 2 + 5 * 2=-6 \\ -4+10=-6 \\ 6=-6 \\ false \\ \\ \hbox{the second equation:} \\ 4 * 2-2 * 2=4 \\ 8-4=4 \\ 4=4 \\ true \\ \\ \hbox{(2,2) satisfies only one of the equations} \\ \hbox{so it's not a solution to the system of equations}`

c.

`5x-2y=-6 \\ 3x-4y=2 \\ \\ \hbox{the first equation:} \\ 5 * 2 - 2 * 2=-6 \\ 10-4=-6 \\ 6=-6 \\ false \\ \\ \hbox{the second equation:} \\ 3 * 2 - 4 * 2=2 \\ 6-8=2 \\ -2=2 \\ false \\ \\ \hbox{(2,2) satisfies none of the equations} \\ \hbox{so it's not a solution to the system of equations}`

d.

`2x+3y=10 \\ 4x+5y=18 \\ \\ \hbox{the first equation:} \\ 2 * 2 + 3 * 2=10 \\ 4+6=10 \\ 10=10 \\ true \\ \\ \hbox{the second equation:} \\ 4 * 2 + 5 * 2 =18 \\ 8+10=18 \\ 18=18 \\ \\ \hbox{(2,2) satisfies both of the equations} \\ \hbox{so it is a solution to the system of equations}`

The answer is D.