Solve the system of equations using the substitution method. x=3+12y - 2x-y=3

We have two equations x = 3+12y and - 2x-y = 3.

In Substitution method, we simplify an expression for one variable and then substitute it into second equation and solve for another variable. Let's solve it below.

x = 3+12y

We can plug it into second equation and solve it for y.

-2 (3+12y) - y = 3

-6 - 24y - y = 3

-25y = 3 + 6

-25y = 9

y = 9 / (-25) = - 9/25

Now we can plug it into first equation and solve for x.

x = 3 + 12 (-9/25)

x = 3 - 108/25

x = (75-108) / 25

x = - 33/25

Hence, solution to the system of equations is (x, y) = (-9/25, - 33/25).

x = - 33/25

y = - 9/25

Step-by-step explanation:

We have the equations

x = 3 + 12y (i)

-2x-y = 3 (ii)

To use the substitution method. We produce equation (i) in equation (ii)

So, we have:

-2 (3 + 12y) - y = 3

Now we clear for y'

-6-24y-y = 3

-25y = 9

y = - 9/25

Now we introduce the value of y into equation (i) and get the value of x

x = 3 + 12 (-9/25)

x = - 33/25