(2)/(3)*y-6=-(1)/(2)*x
(1)/(2)*y-(3x)/(4)=0
Multiply -(1)/(2) by x to get -(x)/(2).
(2)/(3)*y-6=-(x)/(2)
Multiply (2)/(3) by y to get (2y)/(3).
(2y)/(3)-6=-(x)/(2)
Multiply (1)/(2) by y to get
/(2).
/(2)-(3x)/(4)=0
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.
(2y)/(3)=6-(x)/(2)
Move all terms not containing y to the right-hand side of the equation.
(2y)/(3)=-(x)/(2)+6
Multiply each term in the equation by 3.
(2y)/(3)*3=-(x)/(2)*3+6*3
Simplify the left-hand side of the equation by canceling the common factors.
2y=-(x)/(2)*3+6*3
Simplify the right-hand side of the equation by simplifying each term.
2y=-(3x)/(2)+18
Divide each term in the equation by 2.
(2y)/(2)=-(3x)/(2)*(1)/(2)+(18)/(2)
Simplify the left-hand side of the equation by canceling the common factors.
y=-(3x)/(2)*(1)/(2)+(18)/(2)
Simplify the right-hand side of the equation by simplifying each term.
y=-(3x)/(4)+9
Replace all occurrences of y with the solution found by solving the last equation for y. In this case, the value substituted is -(3x)/(4)+9.
(-(3x)/(4)+9)/(2)-(3x)/(4)=0
Divide each term in the numerator by the denominator.
-(3x)/(4)/(2)+(9)/(2)-(3x)/(4)=0
Convert the multiple level fraction to a set of regular fractions by multiplying by the reciprocal of the denominator.
-(3x)/(8)+(9)/(2)-(3x)/(4)=0
Find the LCD (least common denominator) of -(3x)/(8)-(3x)/(4)-(9)/(2).
Least common denominator: 8
Multiply each term in the equation by 8 in order to remove all the denominators from the equation.
-(3x)/(8)*8-(3x)/(4)*8=-(9)/(2)*8
Simplify the left-hand side of the equation by canceling the common factors.
-9x=-(9)/(2)*8
Simplify the right-hand side of the equation by simplifying each term.
-9x=-36
Divide each term in the equation by -9.
-(9x)/(-9)=-(36)/(-9)
Simplify the left-hand side of the equation by canceling the common factors.
y=-(3x)/(4)+9_x=-(36)/(-9)
Simplify the right-hand side of the equation by simplifying each term.
x=4
Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is 4.
y=-(3(4))/(4)+9
Multiply -3 by 4 in the numerator.
y=(-3*4)/(4)+9
Multiply -3 by 4 to get -12.
y=(-12)/(4)+9
Move the minus sign from the numerator to the front of the expression.
y=-(12)/(4)+9
Reduce the expression -(12)/(4) by removing a factor of 4 from the numerator and denominator.
y=-3+9
Add 9 to -3 to get 6.
y=6
This is the solution to the system of equations.
y=6
x=4
Hope I explained thoroughly enough.
2x+2y-8=0
2x+1=y
You must use subsitution to solve for BOTH x and y.
x=1
y=3
Can x=-4 than y=-4??
Yes.
