find the points of intersection between x^2+y^2=45 and -3x+y=15​

Step-by-step answer:Given:Circle C1: x^2+y^2 = 45Line L1: -3x+y=15Need to find the points of intersection.Solution:basically we need to solve for the roots of equations C1 and L1.Here, we can use substitution of L1 into C1.Rewrite L1 as : y=3x+15substitute into C1:x^2+(3x+15)^2 = 45Expandx^2 + 9x^2+90x+225 = 45Rearrange terms:10x^2+90x+180 = 0Simplifyx^2+9x+18 = 0Factor (x+6)(x+3) = 0so x=-6 or x=-3Back-substitute x into L1 to calculate y:x=-6, y=3*x+15 = 3(-6)+15 = -3  => (-6,-3)x=-3, y=3*x+15 = 3(-3) + 15 = 6 => (-3, 6)Therefore the intersection points are (-6,-3) and (-3,6)Check using equation C1:(-6)^2+(-3)^2 = 36+9 = 45  ok(-3)^2+(6)^2 = 9 + 36 = 45 okCheck using equation L1:Point (-6,-3) : y = 3x+15 = 3(-6) +15 = -3  okPoint (-3,6) : y = 3x+15 = 3(-3)+15 = 6 ok.