Question 391121: use combinations and solve:
3y=5x+15
6x=2y-18
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! 3y=5x+15_6x=2y-18
Divide each term in the equation by 3.
(3y)/(3)=(5x)/(3)+(15)/(3)_6x=2y-18
Simplify the left-hand side of the equation by canceling the common factors.
y=(5x)/(3)+(15)/(3)_6x=2y-18
Simplify the right-hand side of the equation by simplifying each term.
y=(5(x+3))/(3)_6x=2y-18
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is (5(x+3))/(3).
y=(5(x+3))/(3)_6x=2((5(x+3))/(3))-18
Multiply 5 by each term inside the parentheses.
y=(5x+15)/(3)_6x=2((5(x+3))/(3))-18
Divide each term in the numerator by the denominator.
y=(5x)/(3)+(15)/(3)_6x=2((5(x+3))/(3))-18
Reduce the expression (15)/(3) by removing a factor of 3 from the numerator and denominator.
y=(5x)/(3)+5_6x=2((5(x+3))/(3))-18
Multiply 5 by each term inside the parentheses.
y=(5x)/(3)+5_6x=2((5x+15)/(3))-18
Divide each term in the numerator by the denominator.
y=(5x)/(3)+5_6x=2((5x)/(3)+(15)/(3))-18
Reduce the expression (15)/(3) by removing a factor of 3 from the numerator and denominator.
y=(5x)/(3)+5_6x=2((5x)/(3)+5)-18
Multiply 2 by each term inside the parentheses.
y=(5x)/(3)+5_6x=(10x)/(3)+10-18
Subtract 18 from 10 to get -8.
y=(5x)/(3)+5_6x=(10x)/(3)-8
Since (10x)/(3) contains the variable to solve for, move it to the left-hand side of the equation by subtracting (10x)/(3) from both sides.
y=(5x)/(3)+5_6x-(10x)/(3)=-8
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 3. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
y=(5x)/(3)+5_6x*(3)/(3)-(10x)/(3)=-8
Complete the multiplication to produce a denominator of 3 in each expression.
y=(5x)/(3)+5_(18x)/(3)-(10x)/(3)=-8
Combine the numerators of all expressions that have common denominators.
y=(5x)/(3)+5_(18x-10x)/(3)=-8
Combine all like terms in the numerator.
y=(5x)/(3)+5_(8x)/(3)=-8
Multiply each term in the equation by 3.
y=(5x)/(3)+5_(8x)/(3)*3=-8*3
Simplify the left-hand side of the equation by canceling the common factors.
y=(5x)/(3)+5_8x=-8*3
Multiply -8 by 3 to get -24.
y=(5x)/(3)+5_8x=-24
Divide each term in the equation by 8.
y=(5x)/(3)+5_(8x)/(8)=-(24)/(8)
Simplify the left-hand side of the equation by canceling the common factors.
y=(5x)/(3)+5_x=-(24)/(8)
Simplify the right-hand side of the equation by simplifying each term.
y=(5x)/(3)+5_x=-3
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is -3.
y=(5(-3))/(3)+5_x=-3
Multiply 5 by -3 in the numerator.
y=(5*-3)/(3)+5_x=-3
Multiply 5 by -3 to get -15.
y=(-15)/(3)+5_x=-3
Move the minus sign from the numerator to the front of the expression.
y=-(15)/(3)+5_x=-3
Reduce the expression -(15)/(3) by removing a factor of 3 from the numerator and denominator.
y=-5+5_x=-3
Add 5 to -5 to get 0.
y=0_x=-3
This is the solution to the system of equations.
y=0_x=-3
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