How do you solve the system x2+y2=5 and y=3x+5? Precalculus Solving Systems of Two Equations Solving by Substitution 1 Answer Shwetank Mauria Aug 28, 2016 Solution set is (−2,−1) or (−1,2) Explanation: As y=3x+5, x2+y2=5 ⇔x2+(3x+5)2=5 or x2×9x2+2×3x×5+25=5 or 10x2+30x+20=0 or dividing by 10, we get x2+3x+2=0 or x2+x+2x×2=0 or x(x+1)+2(x+1)=0 or (x+2)(x+1)=0 i.e. x=−2 or x=−1 Hence y=3×(−2)+5=−1 or y=3×(−1)+5=2 Hence solution set is (−2,−1) or (−1,2) Answer link Related questions What is a system of equations? What does it mean to solve a system of equations by substitution? How do I use substitution to find the solution of the system of equations c+3d=8 and c=4d−6? How do you write a system of linear equations in two variables? How does a system of linear equations have no solution? How many solutions can a system of linear equations have? What is the final step of completing a solve by substitution problem? How do I use substitution to find the solution of the system of equations 4x+3y=7 and 3x+5y=8? How do I use substitution to find the solution of the system of equations y=2x+1 and 2y=4x+2? How do I use substitution to find the solution of the system of equations y=13x+73 and... See all questions in Solving by Substitution Impact of this question 4406 views around the world You can reuse this answer Creative Commons License