Hi! Can someone solve these for me pls?
Y=10/x
y=1/2x+4
solve for x and y
thanks
Hello! Sure, I can help you solve these equations. To find the values of x and y, we need to solve the equations simultaneously. Let's start with the first equation:
Y = 10/x
Since the value of y differs by capitalization, I will assume you meant y in the equation. In that case:
y = 10/x
Now, let's move on to the second equation:
y = (1/2)x + 4
To solve for x and y, we can use substitution or elimination method. Let's use substitution, where we express y in terms of x from one equation and substitute it into the other equation.
First, rearrange the second equation to solve for y:
y = (1/2)x + 4
Now, substitute this value of y into the first equation:
(1/2)x + 4 = 10/x
To get rid of the fraction, we can multiply through by the common denominator, which is 2x:
x * (1/2)x + 4 * 2x = 10
Simplify the equation:
(x^2)/2 + 8x = 10
To make it easier to solve, let's multiply through by 2 to get rid of the denominator:
x^2 + 16x = 20
Rearrange the equation:
x^2 + 16x - 20 = 0
Now, we have a quadratic equation. To solve it, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 1, b = 16, and c = -20. Substituting these values into the quadratic formula, we get:
x = (-16 ± √(16^2 - 4 * 1 * -20))/(2 * 1)
Simplify further:
x = (-16 ± √(256 + 80))/2
x = (-16 ± √336)/2
Now, we can calculate the two possible values of x:
x = (-16 + √336)/2 or x = (-16 - √336)/2
Using a calculator, we get approximately:
x = (-16 + √336)/2 ≈ 1.47 or x = (-16 - √336)/2 ≈ -17.47
Now we have values for x. To find corresponding values for y, we can substitute these values back into either of the original equations. Let's use the first equation:
y = 10/x
For x = 1.47, we have:
y = 10/1.47 ≈ 6.80
And for x = -17.47, we have:
y = 10/(-17.47) ≈ -0.57
Therefore, the solutions to the system of equations are approximately:
x ≈ 1.47, y ≈ 6.80 and x ≈ -17.47, y ≈ -0.57
I hope this explanation helps! Let me know if you have any further questions.