Answer:
C.
Step-by-step explanation:
We are going to solve it with substitution, that is, we are going to clear one variable and then replace it in the other equation. Then,
[tex]3x + 2y = 12[/tex]
[tex]3x = 12-2y[/tex]
[tex]x = \frac{12-2y}{3}[/tex]
[tex]x = \frac{12}{3}-\frac{2y}{3}[/tex]
[tex]x = 4-\frac{2y}{3}.[/tex]
Now, we replace that x value in the equation 6x + 3y = 21:
[tex]6(4-\frac{2y}{3}) + 3y = 21[/tex]
[tex]24-\frac{12y}{3} + 3y = 21[/tex]
[tex]24-4y + 3y = 21[/tex]
[tex]24-y = 21[/tex]
[tex]-y = 21-24[/tex]
[tex]-y = -3[/tex]
[tex]y = 3.[/tex]
Finally, we replace the y value found to find x.
[tex]x = 4-\frac{2*3}{3}[/tex]
[tex]x = 4-2[/tex]
[tex]x = 2.[/tex]
So, the solution is (x,y)=(2,3). Then, the answer is C.
