Example Question - value of y
Here are examples of questions we've helped users solve.
Finding the Value of y with Given x
To find the value of \( y \) using the known value of \( x \), which is \( -\frac{1}{2} \), we should substitute \( x \) into one of the original equations. Let's use the second equation for this example: \( 3x + y = 2 \) Now we substitute \( x \) with \( -\frac{1}{2} \): \( 3(-\frac{1}{2}) + y = 2 \) Solve for \( y \): \( -\frac{3}{2} + y = 2 \) \( y = 2 + \frac{3}{2} \) \( y = \frac{4}{2} + \frac{3}{2} \) \( y = \frac{7}{2} \) So the value of \( y \) is \( \frac{7}{2} \). Therefore, the correct approach is to use the second option (B), "Input the value of \( x \) into either of the original equations."
Solving a Cubic Equation with a Given Value of x
The image shows two equations: 1) \( y = x^3 + 3x^2 - 24x + b \) 2) \( x_0 = 2 \) It appears that you have been provided with a cubic equation and a value for \( x_0 \), which typically would suggest either finding the value of y when \( x = x_0 \), or determining a constant in the equation, like 'b', based on some additional information about \( x_0 \). However, the context or the specific question you need to solve with these equations is not given. If the problem is to find the corresponding y-value (let's call it \( y_0 \)) when \( x = x_0 \), then we would substitute \( x = 2 \) into the first equation: \( y_0 = (2)^3 + 3(2)^2 - 24(2) + b \) \( y_0 = 8 + 3(4) - 48 + b \) \( y_0 = 8 + 12 - 48 + b \) \( y_0 = 20 - 48 + b \) \( y_0 = -28 + b \) So the \( y_0 \) value when \( x = 2 \) depends on the value of 'b'. However, if b is what you're supposed to find, then there is missing information. There needs to be additional information about the graph or a specific y-value when \( x = x_0 \) to find 'b'. If that's the case, please provide the additional information so I can assist further.
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