Question

Solve algebraically the simultaneous equations X^2 + Y^2 =25 Y-2X = 5

Answer 1

Answer:

Therefore the solutions are

$x=0\\and\\ y =5\\\\Or\\\\x=-4\\and\\y=-3$

Step-by-step explanation:

Given:

$x^{2} + y^{2} =25$ .........( 1 )

$y-2x = 5\\y=2x+5$     ................( 2 )

To Find:

x = ?

y = ?

Solution:

Substituting ' y ' in Equation  1 we get

$x^{2}+(2x+5)^{2} =25$

Using identity (A+B)²=A²+2AB+B² we get

$x^{2}+4x^{2}+20x+25=25\\\\5x^{2}+20x=0\\5x(x+4)=0\\5x=0\ or\ x+4=0\\x=0\ or\ x= -4$

Now Substitute x =0 in equation 2 we get

$y=2\times 0+5=5$

Or

Now Substitute x =-4 in equation 2 we get

$y=2\times -4+5=-3$

Therefore the solutions are

$x=0\\and\\ y =5\\\\Or\\\\x=-4\\and\\y=-3$