Question 67·Easy·Nonlinear Equations in One Variable; Systems in Two Variables
The system of equations is
If is positive, what is the value of ?
For systems where one equation is a simple quadratic like and you are told whether is positive or negative, first solve the quadratic and pick the correct sign. Then substitute that value into the linear equation to find , and finally compute whatever combination of and the problem asks for (such as ). This direct substitution approach is faster and less error-prone than trying to work from the answer choices.
Hints
Use the equation with x^2 first
Start with . If is positive, what number squared equals 49?
Use x to find y
Once you know the positive value of , substitute it into to find the corresponding value of .
What does xy represent?
After you have both and , remember that means the product of and . Multiply them to get the final value.
Desmos Guide
Graph the equations
In one expression line, type x^2 = 49. In another line, type y = 2x - 5. Desmos will show two vertical lines (for at and ) and a slanted line for .
Find the intersection with positive x
Click the point where the line intersects the vertical line with positive . The coordinates of this point give the values of and that satisfy both equations with positive.
Compute xy in Desmos
In a new expression line, type the product of the coordinates you found (for example, something like 7*9, using the actual - and -values from the intersection). The number Desmos displays is the value of .
Step-by-step Explanation
Solve for x using x^2 = 49
From , take the square root of both sides:
Because the problem states that is positive, we choose and ignore . So .
Find y using y = 2x - 5
Substitute into the equation :
So when .
Compute the product xy
Now multiply and :
Therefore, , which corresponds to choice C.