NapkinCalc

Algebra 1

Systems of equations

continues from lesson 2 — values defined earlier in the course stay live here

Two unknowns need two equations. Solve 2x + y = 8 and x − y = 1 by elimination: add the equations and y cancels — 3x = 9.

xs=8+13x_{s} = \frac{8 + 1}{3} = 33 add the equations: (2x + y) + (x − y) = 8 + 1
ys=xs−1y_{s} = x_{s} - 1 = 22 back-substitute into x − y = 1
✓ pass abs(2⋅xs+ys−8)<10−9\mathrm{abs}\left(2 \cdot x_{s} + y_{s} - 8\right) < 10^{-9} first equation holds
✓ pass abs(xs−ys−1)<10−9\mathrm{abs}\left(x_{s} - y_{s} - 1\right) < 10^{-9} second equation holds