Respuesta :
Answer:
each balloon costs- $1; each banner costs- $2
Step-by-step explanation:
Answer: the cost of each balloon is $1, the cost of each banner is $2.
Step-by-step explanation:
Let the cost of each balloon is x, and the cost of each banner is y.
Hence,
[tex]\displaystyle\\\left \{ {{3x+2y=7\ \ \ \ (1)} \atop {6x+3y=12\ \ \ \ (2)}} \right. \\[/tex]
We multiply equation (1) by -2:
[tex]\displaystyle\\\left \{ {{-6x-4y=-14} \atop {6x+3y=12}} \right. \\[/tex]
Let's sum up these equations:
[tex]-y=-2\\[/tex]
Multiply both sides of the equation by -1:
[tex]y=2.\\[/tex]
We substitute the value of y into equation (1):
[tex]3x+2*2=7\\3x+4=7\\3x+4-4=7-4\\3x=3\\[/tex]
Divide both sides of the equation by 3:
[tex]x=1.[/tex]
