How do you find the exact solutions to the system #y-x=1# and #x^2+y^2=25#? Precalculus Solving Systems of Two Equations Solving by Substitution 1 Answer Andrea S. Nov 25, 2016 You substitute #y# as function of #x# in the equation of higher degree, using the equation of lower degree, then you solve the former. Explanation: #y-x=1 => y=1+x# Then #x^2+y^2=25# #x^2 +(1+x)^2 = 25# #2x^2+2x+1=25# #2x^2+2x-24 = 0# #x= (-2 +-sqrt(4+192))/4=(-2+-14)/4# #x_1=-4# #x_2=3# and #y_1=-3# #y_2=4# 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 4115 views around the world You can reuse this answer Creative Commons License