Question

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

Answer 1

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).

Answer 2

x = -33/25

y = -9/25

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