Question 167814: Solve each system by the substitution method.
3x + y = 2
-x – 3y = 6
Answer by salvyb(3)   (Show Source):
You can put this solution on YOUR website! 3x+y=2_-x-3y=6
Since 3x does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 3x from both sides.
y=-3x+2_-x-3y=6
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is -3x+2.
y=-3x+2_-x-3(-3x+2)=6
Multiply -3 by each term inside the parentheses.
y=-3x+2_-x+(9x-6)=6
Since -x and 9x are like terms, subtract 9x from -x to get 8x.
y=-3x+2_8x-6=6
Since -6 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 6 to both sides.
y=-3x+2_8x=6+6
Add 6 to 6 to get 12.
y=-3x+2_8x=12
Divide each term in the equation by 8.
y=-3x+2_(8x)/(8)=(12)/(8)
Simplify the left-hand side of the equation by canceling the common terms.
y=-3x+2_x=(12)/(8)
Simplify the right-hand side of the equation by simplifying each term.
y=-3x+2_x=(3)/(2)
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is (3)/(2).
y=-3((3)/(2))+2_x=(3)/(2)
Multiply -3 by each term inside the parentheses.
y=-(9)/(2)+2_x=(3)/(2)
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 2. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
y=2*(2)/(2)-(9)/(2)_x=(3)/(2)
Complete the multiplication to produce a denominator of 2 in each expression.
y=(4)/(2)-(9)/(2)_x=(3)/(2)
Combine the numerators of all fractions that have common denominators.
y=(4-9)/(2)_x=(3)/(2)
Subtract 9 from 4 to get -5.
y=(-5)/(2)_x=(3)/(2)
Move the minus sign from the numerator to the front of the expression.
y=-(5)/(2)_x=(3)/(2)
This is the solution to the system of equations.
y=-(5)/(2)
x=(3)/(2)
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