Answer:
In the form of (x,y) there are 2 solutions:
(-3,4)
(-24/5, -7/5)
Step-by-step explanation:
First isolate one of the letters (for me I'm using the y of equation 2 because it's easier to solve)
[tex]y-3x=13\\y=13+3x[/tex]
Now that we have y isolated, substitute y in equation 1 with the equation we got previously (y=13+3x)
[tex]x^2+(13+3x)^2=25[/tex]
Now simplify:
[tex]x^2+(13+3x)^2=25\\x^2+9x^2+78x+169=25\\10x^2+78x+169=25[/tex]
Now turn the equation into ax^2+bx+c=0 form by transferring 25 to the other side of the equation:
[tex]10x^2+78x+169=25\\10x^2+78x+169-25=0\\10x^2+78x+144=0[/tex]
Using the quadratic formula we will have the 2 following values:
[tex]x=-3[/tex]
[tex]x=-\frac{24}{5}[/tex]
Substitute the following values into any equation you want (this time I'll pick equation 2 again since its the easiest to solve)
[tex]y-3x=13\\y-3(-3)=13\\y-(-9)=13\\y+9=13\\y=13-9\\y=4[/tex]
[tex]y-3x=13\\y-3(-\frac{24}{5})=13\\y-(-\frac{72}{5})=13\\y+\frac{72}{5}=13\\y=13-\frac{72}{5}\\y=-\frac{7}{5}[/tex]
