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Pachacha [2.7K]
3 years ago
12

Solve the following system. x2 + y 2= 25 2x + y = 10 The solution set

Mathematics
1 answer:
anzhelika [568]3 years ago
8 0

Answer: {(5,0), (3,4)}

Step-by-step explanation:

You can apply the Substitution method:

- Solve for y from the second equation.

- Substitute into the first equation and solve for x.

Then:

y=10-2x

x^2+y^2=25\\x^2+(10-2x)^2=25\\

(Remember that: (a\±b)^2=a^2\±2ab+b^2)

x^2+(10^2-2(10)(2x)+(2x)^2)=25\\x^2+100-40x+4x^2=25\\5x^2-40x+75=0\\x^2-8x+15=0\\(x-5)(x-3)=0\\\\x=5\\x=3

Substitute the values obtained into one of the original equation and solve for y:

2(5)+y=10\\10+y=10\\y=0\\\\2(3)+y=10\\6+y=10\\y=4

The solution set is: {(5,0), (3,4)}

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