solve by the substitution method
3x + 6y = 27
-2x + y = 12
what is the solution of the system..(type an ordered pair, or N if there is no solution)
has to be like (3,5)please help me
To solve the system of equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the second equation, "-2x + y = 12," for "y" in terms of "x":
y = 2x + 12.
Step 2: Substitute the expression found in Step 1 into the other equation.
Replace the "y" in the first equation, "3x + 6y = 27," with "2x + 12" from Step 1:
3x + 6(2x + 12) = 27.
Step 3: Simplify and solve the resulting equation.
Expand the brackets and combine like terms:
3x + 12x + 72 = 27.
15x + 72 = 27.
15x = 27 - 72.
15x = -45.
x = -45/15.
x = -3.
Step 4: Substitute the value of "x" into one of the original equations to solve for the other variable.
Let's substitute x = -3 into the second equation, "-2x + y = 12":
-2(-3) + y = 12.
6 + y = 12.
y = 12 - 6.
y = 6.
Therefore, the solution to the system of equations is (x, y) = (-3, 6).