Answer:
Option C is correct
the solution for the given system of equation is, (0, -5) and (-4, 3)
Step-by-step explanation:
Using identity:
[tex](a+b)^2=a^2+b^2+2ab[/tex]
Given the equation:
[tex]x^2+y^2=25[/tex] .....[1]
[tex]2x+y=-5[/tex] .....[2]
We can write [2] as:
[tex]y = -5-2x[/tex]
Substitute this in [1] we have;
[tex]x^2+(-5-2x)^2=25[/tex]
Using identity rule;
[tex]x^2+25+4x^2+20x = 25[/tex]
Combine like terms;
[tex]5x^2+20x+25 = 25[/tex]
Subtract 25 from both sides we have;
[tex]5x^2+20x=0[/tex]
⇒[tex]5x(x+4)=0[/tex]
By zero product property we have;
x = 0 and x+4 = 0
x = 0 and x = -4
Substitute these in [2] we have;
for x = 0
2(0)+y = -5
⇒[tex]y = -5[/tex]
For x = -4 ,
[tex]2(-4)+y = -5[/tex]
-8+y = -5
add 8 to both sides we have;
y = 3
Therefore, the solution for the given system of equation is, (0, -5) and (-4, 3)
