Solve using the substitution method 6x-3y=18, 6x+3y=-12
Substitution:
Rewrite each as:
6x=3y+18
6x=-12-3y
Since they are both 6x, then
3y+18=-12-3y
=>
6y=-30
y=-5
and
x=(3*(-5)+18)/6=1/2
By elimination (easier in this case)
Add the two equations:
6x-3y + 6x+3y = 18 -12
12x=6
x=1/2
-3y=18-6*(1/2)
y=-5
To solve the system of equations using the substitution method, follow these steps:
Step 1: Start by choosing one of the equations to solve for one variable in terms of the other variable. Let's choose the first equation, 6x - 3y = 18.
Step 2: Solve the chosen equation for one variable. In this case, we will solve for x in terms of y.
6x - 3y = 18
6x = 3y + 18
x = (3y + 18)/6
x = (y + 6)/2
Now we have x in terms of y.
Step 3: Substitute the expression for x into the other equation. We will use the second equation, 6x + 3y = -12.
6[(y + 6)/2] + 3y = -12
3(y + 6) + 3y = -12
3y + 18 + 3y = -12
6y + 18 = -12
6y = -12 - 18
6y = -30
y = -30/6
y = -5
Step 4: Substitute the value of y back into the expression we found for x.
x = (y + 6)/2
x = (-5 + 6)/2
x = 1/2
After performing the substitutions, we find that the solution to the system of equations is x = 1/2 and y = -5.