# Manipulating Equations: Substracting two equations

I was wondering why I fail to substract two equations using thread, while it works properly, as described here for additions.

Example: Let a system of equations be given:

eq1 = a + b == c
eq2 = a - b == c


Thread[eq1 + eq2, Equal]


which gives the correct result:

a == c


However, when I substract the two eqations (1)-(2) via

Thread[eq1 - eq2, Equal]


I get

a + b - (a - b == c) == c - (a - b == c)


and simplifying it gives me the first equation.

a + b == c


Can anyone tell me why Thread does not work with a minus sign? Sorry if this is a trivial question.

• You could use SubtractSides[eq1, eq2]. – b.gates.you.know.what Nov 21 '18 at 11:07
• Thanks, that solves the problem more efficiently. It also works if I multiply the equation by -1 via Thread[eq1*-1,Equal] and add it via Thread, but I was wondering why Thread fails. – Paul Saturday Nov 21 '18 at 11:25
• By entering Subtract[eq1, eq2] // FullForm you see that it actually evaluates to Plus[eq1,Times[-1,eq2]], and the effect is that the equation will be multiplied by -1 and the threading operates again on the outer Plus part, which gives the result you see. – Thies Heidecke Nov 21 '18 at 13:02