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