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Answer:
x = 2 and y = 7
Step-by-step explanation:
The given equations are :
[tex]y^2+x^2=53\ ....(1)\\\\y-x=5\ ...(2)[/tex]
Squaring both sides of equation (2)
[tex](y-x)^2=5^2\\\\y^2+x^2-2xy=25\\\\53-2xy=25\ \text{from equation (1)}\\\\2xy=53-25\\\\2xy=28\\\\xy=14\ ...(3)[/tex]
Put the value of y from equation (2)
[tex]x(5+x)=14\\\\5x+x^2-14=0\\\\x=2[/tex]
Put the value of x in equation (2)
y-x = 5
y = 5+x
= 5+2
= 7
Hence, the solution of the given equations are (2,7).