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

Answers

Answer 1

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

a.
$-3x+3y=0 \nx+6y=10 \n \n\hbox{the first equation:} \n-3 * 2+3 * 2=0 \n-6+6=0 \n0=0 \ntrue \n \n\hbox{the second equation:} \n2+6 * 2=10 \n2+12=10 \n14=10 \nfalse \n \n\hbox{(2,2) satisfies only one of the equations} \n\hbox{so it's not a solution to the system of equations}$

b.
$-2x+5y=-6 \n4x-2y=4 \n \n\hbox{the first equation:} \n-2 * 2 + 5 * 2=-6 \n-4+10=-6 \n6=-6 \nfalse \n \n\hbox{the second equation:} \n4 * 2-2 * 2=4 \n8-4=4 \n4=4 \n true \n \n\hbox{(2,2) satisfies only one of the equations} \n\hbox{so it's not a solution to the system of equations}$

c.
$5x-2y=-6 \n3x-4y=2 \n \n\hbox{the first equation:} \n5 * 2 - 2 * 2=-6 \n10-4=-6 \n6=-6 \nfalse \n \n\hbox{the second equation:} \n3 * 2 - 4 * 2=2 \n6-8=2 \n-2=2 \nfalse \n \n\hbox{(2,2) satisfies none of the equations} \n\hbox{so it's not a solution to the system of equations}$

d.
$2x+3y=10 \n4x+5y=18 \n \n\hbox{the first equation:} \n2 * 2 + 3 * 2=10 \n4+6=10 \n10=10 \ntrue \n \n\hbox{the second equation:} \n4 * 2 + 5 * 2 =18 \n8+10=18 \n18=18 \n \n\hbox{(2,2) satisfies both of the equations} \n\hbox{so it is a solution to the system of equations}$

The answer is D.

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