Respuesta :
Answer:
[tex](8,-1)[/tex]
Step-by-step explanation:
The given system is:
[tex]3x+3y=21[/tex]
[tex]6x+12y=36[/tex]
Since I prefer to use smaller numbers I'm going to divide both sides of the first equation by 3 and both sides of the equation equation by 6.
This gives me the system:
[tex]x+y=7[/tex]
[tex]x+2y=6[/tex]
We could solve the first equation for [tex]x[/tex] and replace the second [tex]x[/tex] with that.
Let's do that.
[tex]x+y=7[/tex]
Subtract [tex]y[/tex] on both sides:
[tex]x=7-y[/tex]
So we are replacing the second [tex]x[/tex] in the second equation with [tex](7-y)[/tex] which gives us:
[tex](7-y)+2y=6[/tex]
[tex]7-y+2y=6[/tex]
[tex]7+y=6[/tex]
[tex]y=6-7[/tex]
[tex]y=-1[/tex]
Now recall the first equation we arranged so that [tex]x[/tex] was the subject. I'm referring to [tex]x=7-y[/tex].
We can now find [tex]x[/tex] given that [tex]y=-1[/tex] using the equation [tex]x=7-y[/tex].
Let's do that.
[tex]x=7-y[/tex] with [tex]y=-1[/tex]:
[tex]x=7-(-1)[/tex]
[tex]x=7+1[/tex]
[tex]x=8[/tex]
So the solution is (8,-1).
We can check this point by plugging it into both equations.
If both equations render true for that point, then we have verify the solution.
Let's try it.
[tex]3x+3y=21[/tex] with [tex](x,y)=(8,-1)[/tex]:
[tex]3(8)+3(-1)=21[/tex]
[tex]24+(-3)=21[/tex]
[tex]21=21[/tex] is a true equation so the "solution" looks promising still.
[tex]6x+12y=36[/tex] with [tex](x,y)=(8,-1)[/tex]:
[tex]6(8)+12(-1)=36[/tex]
[tex]48+(-12)=36[/tex]
[tex]36=36[/tex] is also true so the solution has been verified since both equations render true for that point.
3x + 3y = 21
6x + 12y = 36
[tex]\frac{6x + 12y=36}{6} \\\\x+2y=6\\\\x=6-2y\\----------\\3(6-2y)+3y=21\\\\18-6y+3y=21\\\\18-3y=21\\\\-1(-3y=3)\\\\3y=-3\\\\y=-1[/tex]
[tex]3x+3y=21\\\\3x+3(-1)=21\\3x-3=21\\3x=24\\x=8[/tex]
x = 8 and y = -1
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