Solve the system of equations: 1. x + xy + y = 5 2. x^2 + xy + y^2 = 7
Solve the system of equations:
1. x + xy + y = 5
2. x^2 + xy + y^2 = 7
1. x + xy + y = 5
2. x^2 + xy + y^2 = 7
Snap Your Questions, Uncover the Solutions
info@snapandsolve.comTo solve the system of equations, we can use substitution or elimination. Let's use substitution:
From equation 1: x + xy + y = 5, we can express x in terms of y:
x(1 + y) = 5 - y
x = (5 - y) / (1 + y)
Substitute x in equation 2: x^2 + xy + y^2 = 7
[(5 - y) / (1 + y)]^2 + [(5 - y) / (1 + y)]y + y^2 = 7
Simplify and solve for y:
(25 - 10y + y^2) / (1 + y)^2 + (5y - y^2) / (1 + y) + y^2 = 7
Multiply through by (1 + y)^2 to clear the denominators:
25 - 10y + y^2 + (5y - y^2)(1 + y) + y^2(1 + y)^2 = 7(1 + y)^2
Expand and simplify:
25 - 10y + y^2 + 5y + 5y^2 - y^3 + y^2 + 2y^3 + y^4 = 7 + 14y + 7y^2
Combine like terms:
y^4 + y^3 - 11y^2 - 19y + 18 = 0
This is a quartic equation that can be solved using numerical methods or graphing to find the roots. Let's assume y = 1 is a solution:
Substitute y = 1 back into the expression for x:
x = (5 - 1) / (1 + 1) = 4 / 2 = 2
Check the solution in both equations:
Equation 1: 2 + 2(1) + 1 = 5, which is true.
Equation 2: 2^2 + 2(1) + 1^2 = 7, which is true.
Thus, one solution is (x, y) = (2, 1).
Snap a photo of your homework and get a step-by-step answer in seconds. You can ask follow-up questions until it makes sense.
Solve my question free Math help Find a math tutor© 2026 SnapAndSolve