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Question 388692: y=5+6x and 18x+3y=12
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! SOLVED WITH GRAPHING METHOD
y=5+6x_18x+3y=12
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is 6x+5.
y=6x+5_18x+3(6x+5)=12
Multiply 3 by each term inside the parentheses.
y=6x+5_18x+18x+15=12
Since 18x and 18x are like terms, add 18x to 18x to get 36x.
y=6x+5_36x+15=12
Since 15 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 15 from both sides.
y=6x+5_36x=-15+12
Add 12 to -15 to get -3.
y=6x+5_36x=-3
Divide each term in the equation by 36.
y=6x+5_(36x)/(36)=-(3)/(36)
Simplify the left-hand side of the equation by canceling the common factors.
y=6x+5_x=-(3)/(36)
Simplify the right-hand side of the equation by simplifying each term.
y=6x+5_x=-(1)/(12)
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -(1)/(12).
y=6(-(1)/(12))+5_x=-(1)/(12)
Multiply 6 by each term inside the parentheses.
y=-(1)/(2)+5_x=-(1)/(12)
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=5*(2)/(2)-(1)/(2)_x=-(1)/(12)
Complete the multiplication to produce a denominator of 2 in each expression.
y=(10)/(2)-(1)/(2)_x=-(1)/(12)
Combine the numerators of all fractions that have common denominators.
y=(10-1)/(2)_x=-(1)/(12)
Subtract 1 from 10 to get 9.
y=(9)/(2)_x=-(1)/(12)
This is the solution to the system of equations.
y=(9)/(2)_x=-(1)/(12)
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