Question 26915
To make it a bit easier, I'd rewrite it so every line is in the same form like:
Eq1:{{{d+e-f=5}}}
Eq2:{{{-d+e-f=7}}}
Eq3:{{{-2e+f=-11}}}
Now in this form we can see that we can use combination and add Eq1 & Eq2 to write an equation only in terms of E&F:
{{{2e-2f=12}}}
Now that we have two equations of only two variables (this one & Eq3) we can solve for e & f. Adding this new equation to Eq 3 we get:
{{{-f=1}}}
{{{f=-1}}}
Putting this back into Eq 3 we get:
{{{-2e+f=-11}}}
{{{-2e+-1=-11}}}
{{{-2e=-10}}}
{{{e=5}}}
Now we know e & f, so we can use any equation (in this example Eq 1.) to find d:
{{{d+e-f=5}}}
{{{d+5-(-1)=5}}}
{{{d=-1}}}
Double checks:
Eq1:{{{d+e-f=5}}}={{{-1+5-(-1)=5}}}check.
Eq2:{{{-d+e-f=7}}}={{{-(-1)+5-(-1)=7}}}check.
Eq3:{{{-2e+f=-11}}}={{{-2*5+(-1)=-11}}}check.