Solve this simultaneous equation:
x+3y=2 and x/3+y/2 =1
Please explain step by step so i understand for future reference.
Thankyou x
first, get rid of those pesky fractions and you have
x+3y = 2
2x+3y = 6
now subtract the 1st from the 2nd and you have
x = 4
Then plug that into either equation to find y:
4+3y = 2
y = -2/3
final step: check those values in each of the original equations to make sure you have not made a mistake somewhere.
To solve this system of equations, we can use either the substitution or elimination method.
Let's start with the substitution method:
1. Begin by solving one of the equations for one variable in terms of the other variable. In this case, let's solve the first equation for x:
x = 2 - 3y
2. Substitute the expression for x into the second equation.
(2 - 3y)/3 + y/2 = 1
3. Simplify the equation by multiplying through by the appropriate common denominators:
(2 - 3y)(2) + y(3) = 3(1)
4 - 6y + 3y = 3
4. Combine like terms:
-3y + 4 = 3
5. Isolate the variable by subtracting 4 from both sides of the equation:
-3y = 3 - 4
-3y = -1
6. Divide both sides of the equation by -3 to solve for y:
y = -1 / -3
y = 1/3
7. Substitute the value of y back into either of the original equations. Let's use the first equation:
x + 3(1/3) = 2
x + 1 = 2
8. To find the value of x, subtract 1 from both sides of the equation:
x = 2 - 1
x = 1
Therefore, the solution to the system of equations is x = 1 and y = 1/3.
Using the substitution method, we obtained the solution by solving one equation for one variable and substituting that expression into the other equation. We then solved for the remaining variable and found the values of x and y.
Alternatively, we could have used the elimination method by multiplying one or both equations by appropriate constants to eliminate one variable and then solving for the remaining variable.