Solve each system of linear equation and explain any method you used:
-2/3x+4y=36
y=5x-20
To solve the system of linear equations,
-2/3x + 4y = 36
y = 5x - 20
We can use the method of substitution.
First, we substitute the value of y in the first equation with its equivalent expression from the second equation:
-2/3x + 4(5x - 20) = 36
Next, we simplify the equation by multiplying 4 to each term inside the brackets:
-2/3x + 20x - 80 = 36
To combine the x terms, we find a common denominator for -2/3x and x. The common denominator is 3:
-2/3x + 60/3x - 80 = 36
-2/3x + 60/3x can be simplified to -2/3x + 20x:
-2/3x + 20x - 80 = 36
Now, we combine like terms:
(20x - 2/3x) - 80 = 36
18 2/3x - 80 = 36
To isolate the x term, we add 80 to both sides:
18 2/3x = 116
To convert the mixed number into an improper fraction, we multiply the whole number (18) by the denominator (3) and add the numerator (2), then place it over the denominator:
(18*3 + 2)/3 = 116/3
(54 + 2)/3 = 116/3
56/3 = 116/3
Now that both sides of the equation have the same denominator, we can equate the numerators:
56 = 116
Since the equation 56 = 116 is not true, there is no solution to this system of linear equations. The two lines represented by the equations do not intersect and are parallel to each other.