Question

Choose a system of equations with the same solution as the following system:

4x − 2y = 6
2x + y = 5

A.−4x − 2y = 10
2x − 3y = 21

B.4x + 2y = 10
10x + y = 21

C.−4x − 5y = −1
2x − 6y = 10

D.3x + 2y = 6
9x + y = 17

Answer 1

B

Explanation:

Answer 2

`\large\boxed{B. \left\{\begin{array}{ccc}4x+2y=10\\10x+y=21\end{array}\right}`

Explanation:

`\left\{\begin{array}{ccc}4x-2y=6\\2x+y=5&\text{multiply both sides by 2}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}4x-2y=6\\4x+2y=10\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad8x=16\qquad\text{divide both sides by 8}\\.\qquad x=2\\\\\text{put the value of x to the second equation:}\\\\2(2)+y=5\\4+y=5\qquad\text{subtract 4 from both sides}\\y=1`

`\text{Put the value of x and y to the each equation and check the equalities:}\\\\A.\\-4x-2y=10\\-4(2)-2(1)=10\\-8-2=10\\-10=10\qquad\bold{FALSE}\\\\B.\\4x+2y=10\\4(2)+2(1)=10\\8+2=10\\10=10\qquad\bold{CORRECT}\\10x+y=21\\10(2)+1=21\\20+1=21\\21=21\qquad\bold{CORRECT}\\\\C.\\-4x-5y=-1\\-4(2)-5(1)=-1\\-8-5=-1\\-14=-1\qquad\bold{FALSE}\\\\D.\\3x+2y=6\\3(2)+2(1)=6\\6+2=6\\8=6\qquad\bold{FALSE}`