HELP HELP The sum of the product of 16 and x and the product of 11 and y is 218. The difference of the product of 5 and x and the product of 11 and y is -134. What are the values of x and y?
PLS
use algebra to write the given facts:
16x+11y = 218
5x-11y = -134
adding, we get
21x = 84
and the rest should be no sweat ...
To solve the given system of equations, we'll use the method of substitution. Let's rewrite the equations:
Equation 1: 16x + 11y = 218
Equation 2: 5x - 11y = -134
First, let's solve Equation 2 for x:
5x - 11y = -134
5x = 11y - 134
x = (11y - 134)/5
Now, substitute this expression for x into Equation 1:
16[(11y - 134)/5] + 11y = 218
Simplifying this equation:
(176y - 2144)/5 + 11y = 218
(176y - 2144 + 55y)/5 = 218
231y - 2144 = 1090
Next, solve for y:
231y = 1090 + 2144
231y = 3234
y = 3234/231
y = 14
Now that we have the value of y, substitute it back into Equation 1 to find x:
16x + 11(14) = 218
16x + 154 = 218
16x = 218 - 154
16x = 64
x = 64/16
x = 4
Therefore, the values of x and y are x = 4 and y = 14, respectively.