Answer:
(0.3135, 1.9405) and (-1.9135, -4.7405)
Step-by-step explanation:
[tex]x^2+y^2-2x+4y-11=0[/tex]
[tex]x^2+y^2+4x+2y-9=0[/tex]
Subtracting the equations we get
[tex]-6x+2y-2=0\\\Rightarrow -3x+y-1=0\\\Rightarrow y=1+3x[/tex]
Putting the y value in the first equation
[tex]x^2+(1+3x)^2-2x+4(1+3x)-11=0\\\Rightarrow x^2+1+9x^2+6x-2x+4+12x-11=0\\\Rightarrow 10x^2+16x-6=0\\\Rightarrow 5x^2+8x-3=0[/tex]
[tex]x=\frac{-8+\sqrt{8^2-4\cdot \:5\left(-3\right)}}{2\cdot \:5}, x=\frac{-8-\sqrt{8^2-4\cdot \:5\left(-3\right)}}{2\cdot \:5}\\\Rightarrow x=0.3135, -1.9135[/tex]
[tex]y=1+3x\\\Rightarrow y=1+3(0.3135)\\\Rightarrow y=1.9405[/tex]
[tex]y=1+3x\\\Rightarrow y=1+3(-1.9135)\\\Rightarrow y=-4.7405[/tex]
So, the points of intersection are (0.3135, 1.9405) and (-1.9135, -4.7405)
