Solve the following system of equations. You will type your x value in the first part and the y value in the second part of the question. If the answer if no solution then type NS in both parts and if the the answer is infinite solutions then type I in both parts.
x = 0.7(300 - y)
y = 0.8(300 - x)
What is the x value?
y = 0.8(300 - x)
y = 240 - .8x
x = 0.7(300 - y)
x = 210 - .7y
sub y = 240 - .8x into
x = 210 - .7y
x = 210 - .7(240 - .8x)
x = 210 - 168 + .56x
.44x = 42
x = 42/.44 = 4200/44 = 1050/11
To solve the given system of equations, we will use the method of substitution.
First, let's start by solving one equation for x in terms of y. We can rearrange the first equation as follows:
x = 0.7(300 - y)
Next, substitute this expression for x in the second equation:
y = 0.8(300 - x)
y = 0.8(300 - (0.7(300 - y)))
Now we can simplify and solve for y:
y = 0.8(300 - 0.7(300 - y))
Distribute the 0.7 inside the parentheses:
y = 0.8(300 - 210 + 0.7y)
Simplify the expression inside the parentheses:
y = 0.8(90 + 0.7y)
Multiply 0.8 by 90 and by 0.7y:
y = 72 + 0.56y
To isolate the variable y, subtract 0.56y from both sides:
y - 0.56y = 72
Simplify:
0.44y = 72
Divide both sides by 0.44:
y = 72 / 0.44
Evaluate the division:
y ≈ 163.636
Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:
x = 0.7(300 - y)
Substitute y ≈ 163.636:
x = 0.7(300 - 163.636)
Now we can calculate:
x = 0.7(136.364)
x ≈ 95.454
Therefore, the value of x is approximately 95.454.