How this calculator works
Enter a in ax+by=e, b in ax+by=e, c in cx+dy=f, d in cx+dy=f, e constant, f constant. CalcStack applies the displayed formula and reports each intermediate planning value with the units shown.
Formula / method
x = (ed − bf) ÷ (ad − bc); y = (af − ec) ÷ (ad − bc)
Worked example
2x+3y=13 and x−y=1 solve to x=3.2 and y=2.2.
Assumptions and limitations
The determinant ad−bc is non-zero.
Near-zero determinants can amplify floating-point error; dependent systems need separate treatment.