Respuesta :
Answer:
The answer is [tex]x=3[/tex] and [tex]y=8.[/tex]
Step-by-step explanation:
Given:
3y+10x−54=0
5y−2x−34=0
Now, to solve the system of equations:
[tex]3y+10x-54=0\\\\3y+10x=54\ \ \ ......(1)[/tex]
[tex]5y-2x-34=0\\\\5y-2x=34\ \ \ \ ........(2)[/tex]
So, to multiply the equation (2) by 5 we get:
[tex]25y-10x=170\ \ \ ...(2)[/tex]
Now, to solve the equations by adding both the equations (1) and (2):
[tex]3y+10x+(25y-10x)=170+54\\\\3y+10x+25y-10x=224\\\\28y=224[/tex]
Then, dividing both sides by 28 we get:
[tex]y=8.[/tex]
Now, substituting the value of [tex]y[/tex] in equation (1):
[tex]3y+10x=54\\\\3(8)+10x=54\\\\3\times 8+10x=54\\\\24+10x=54[/tex]
Subtracting both sides by 24 we get:
[tex]10x=30[/tex]
Dividing both sides by 10 we get:
[tex]x=3.[/tex]
Therefore, the answer is [tex]x=3[/tex] and [tex]y=8.[/tex]
