Question 389656: Solve the system of linear equations using the Substitution Method.
x+2y=3
3x-y=-1
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! x+2y=3_3x-y=-1
Since 2y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2y from both sides.
x=-2y+3_3x-y=-1
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -2y+3.
x=-2y+3_3(-2y+3)-y=-1
Multiply 3 by each term inside the parentheses.
x=-2y+3_-6y+9-y=-1
Since -6y and -y are like terms, subtract y from -6y to get -7y.
x=-2y+3_-7y+9=-1
Since 9 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 9 from both sides.
x=-2y+3_-7y=-9-1
Subtract 1 from -9 to get -10.
x=-2y+3_-7y=-10
Divide each term in the equation by -7.
x=-2y+3_-(7y)/(-7)=-(10)/(-7)
Simplify the left-hand side of the equation by canceling the common factors.
x=-2y+3_y=-(10)/(-7)
Simplify the right-hand side of the equation by simplifying each term.
x=-2y+3_y=(10)/(7)
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is (10)/(7).
x=-2((10)/(7))+3_y=(10)/(7)
Multiply -2 by each term inside the parentheses.
x=-(20)/(7)+3_y=(10)/(7)
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 7. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
x=3*(7)/(7)-(20)/(7)_y=(10)/(7)
Complete the multiplication to produce a denominator of 7 in each expression.
x=(21)/(7)-(20)/(7)_y=(10)/(7)
Combine the numerators of all fractions that have common denominators.
x=(21-20)/(7)_y=(10)/(7)
Subtract 20 from 21 to get 1.
x=(1)/(7)_y=(10)/(7)
This is the solution to the system of equations.
x=(1)/(7)_y=(10)/(7)
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