I need to find a solution by substitution method
http://www.purplemath.com/modules/systlin4.htm
To solve a system of equations using the substitution method, follow these steps:
Step 1: Choose one equation to solve for one variable in terms of the other variable. Let's call this equation "Equation 1".
Step 2: Substitute the expression you found from Equation 1 into the other equation in place of the variable you solved for. This will allow you to solve for the other variable.
Step 3: Once you have the value of one variable, substitute it back into either Equation 1 or the other original equation to find the value of the other variable.
Step 4: Check if the solution satisfies all the original equations. If it does, then it is the correct solution. If not, then there may be no solution or an error may have occurred during the calculations.
Here's an example to illustrate the substitution method:
Example:
Solve the system of equations:
Equation 1: 2x + y = 6
Equation 2: x - y = 2
Step 1:
From Equation 2, solve for x in terms of y:
x = y + 2
Step 2:
Substitute x = y + 2 into Equation 1:
2(y + 2) + y = 6
Simplify the equation:
2y + 4 + y = 6
Combine like terms:
3y + 4 = 6
Subtract 4 from both sides:
3y = 2
Divide both sides by 3:
y = 2/3
Step 3:
Substitute y = 2/3 back into Equation 2:
x - 2/3 = 2
Add 2/3 to both sides:
x = 2 + 2/3
x = 8/3
Step 4:
To check the solution, substitute the values of x and y into both original equations:
Equation 1: 2(8/3) + (2/3) = 6 (simplifying the expression gives 16/3 + 2/3 = 18/3 = 6)
Equation 2: (8/3) - (2/3) = 2 (simplifying the expression gives 6/3 = 2)
Since both equations are satisfied by x = 8/3 and y = 2/3, that is the solution.
So, the solution to the system of equations is x = 8/3 and y = 2/3.