use substitution
x/3-y=3
2x+y=25
substitute one equation with y or x
ex: y=-2x+25
substitute that for y in the first equation and solve
x=12
y=1
To solve the system of equations using substitution, we need to follow these steps:
Step 1: Solve one equation for one variable (in terms of the other variable).
Let's solve the first equation for x:
x/3 - y = 3
Multiply both sides by 3 to get rid of the denominator:
3(x/3 - y) = 3(3)
x - 3y = 9
Now we have x expressed in terms of y.
Step 2: Substitute the expression obtained in step 1 into the second equation.
Replace x in the second equation with the expression we found:
2x + y = 25
2(x - 3y) + y = 25
2x - 6y + y = 25
2x - 5y = 25
Step 3: Solve the equation obtained in step 2.
We have a single equation with one variable, which we can solve by isolating the variable:
2x - 5y = 25
2x = 5y + 25
Divide both sides by 2:
x = (5y + 25)/2
Now we have x expressed in terms of y.
Step 4: Substitute the expression obtained in step 3 back into either of the original equations.
Let's substitute it back into the first equation:
x/3 - y = 3
[(5y + 25)/2]/3 - y = 3
Multiply both sides by 2 to get rid of the fraction:
(5y + 25)/3 - 2y = 6
Multiply both sides by 3 to get rid of the denominator:
5y + 25 - 6y = 18
Combine like terms:
-y + 25 = 18
Subtract 25 from both sides:
-y = 18 - 25
-y = -7
Multiply both sides by -1 (to isolate y and change the sign):
y = 7
Step 5: Substitute the value of y obtained in step 4 into either of the expressions found in step 1 or step 3, and solve for the corresponding value of x.
Using the expression found in step 3:
x = (5y + 25)/2
x = (5(7) + 25)/2
x = (35 + 25)/2
x = 60/2
x = 30
Therefore, the solution to the system of equations is x = 30 and y = 7.