solve the system 3x-6y=5 and 2y=4x-6 using substitution method.
from the 2nd
y = 2x-3 after dividing by 2
sub into the first
3x - 6(2x-3) = 5
3x - 12 + 18 = 5
I bet you can finish it from here
To solve the system of equations using the substitution method, we will solve one equation for one variable and substitute it into the other equation.
Step 1: Solve one equation for one variable.
Let's solve the second equation, 2y = 4x - 6, for y:
Divide the whole equation by 2 to isolate y:
y = 2x - 3
Step 2: Substitute the value found into the other equation.
Now let's substitute the value of y, which is 2x - 3, into the first equation, 3x - 6y = 5:
3x - 6(2x - 3) = 5
Step 3: Simplify and solve for x.
Distribute the -6 to get rid of the parentheses:
3x - 12x + 18 = 5
Combine like terms:
-9x + 18 = 5
Subtract 18 from both sides:
-9x = -13
Divide both sides by -9 to solve for x:
x = -13 / -9
x = 13/9
Step 4: Substitute the value of x back into one of the original equations to solve for y.
Substitute x = 13/9 into the equation y = 2x - 3:
y = 2(13/9) - 3
Multiply 2 by 13/9:
y = 26/9 - 27/9
Subtract the fractions:
y = -1/9
The solution to the system of equations is x = 13/9 and y = -1/9.