Question

Which point is the solution to the following system of equations? x2 + y2 = 13 2x - y = 4

Answer 1

Answer with Step-by-step explanation:

2x-y=4 ⇒y=2x-4

x²+y²=13

⇒ x²+(2x-4)²=13

⇒ x²+4x²+16-16x=13

⇒ 5x²-16x+3=0

⇒ 5x²-15x-x+3=0

5x(x-3)-1(x-3)=0

⇒ (5x-1)(x-3)=0

either 5x-1=0 or x-3=0

x=1/5 or x=3

when x=1/5=0.2, y=2/5-4 i.e. y=-3.6

when x=3, y=2

Hence, solution of x²+y²=13 and 2x-y=4 is:

x=0.2,y= -3.6 and x=3,y=2

Answer 2

There are two solutions.
.. (3, 2)
.. (0.2, -3.6)

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