How do you solve the system 6x^2+3y^2=12 and y=-x+2? Precalculus Solving Systems of Two Equations Solving by Substitution 1 Answer Ratnaker Mehta Aug 1, 2016 The Soln. Set ={(0,2), (4/3,2/3)} Explanation: We subst. y from the Second eqn. into the First one, to get, 6x^2+3(2-x)^2=12 :. 6x^2+3(4-4x+x^2)=12 :. 9x^2-12x=12-12=0. :. 3x(3x-4)=0 :. x=0, or, x=4/3 accordingly, y=2, or, 2/3 :. The Soln. Set ={(0,2), (4/3,2/3)} 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=1/3x+7/3 and... See all questions in Solving by Substitution Impact of this question 2131 views around the world You can reuse this answer Creative Commons License