Solving a system of linear equations using the substitution method.
5x+4y=-26
5-x=-6y

Solve for x in 2nd equation
times -1 both sides
x-5=6y
add 5
x=6y+5

sub

5(6y+5)+4y=-26
30y+25+4y=-26
34y+25=-26
minus 25 both sides
34y=-51
divide both sides by 34
y=-3/2
sub back

x=6y+5
x=6(-3/2)+5
x=-18/2+5
x=-9+5
x=-4

(-4,-3/2) is solution

We write x in terms of y in order to substitute using the second equation
-x=-6y-5
x= 6y+5

We substitute what we got above in the first equation 
5(6y+5)+4y=-26

We solve for y
30y+25+4y=-26
34y+25=-26
34y=-51
y=-51/34

Then we plug what we got for y back in our first equation in order to get the value of x as well

x=6(-51/34)+5
x=-4

So the solutions are:
x=-4
y=-1.5