Final answer:
To find the value of 2x+4y given the equations 3x+5y=9 and x+y=5, you must first solve the system of equations to find x and y. By substituting and simplifying, we determine that x = 8 and y = -3. Then, substituting x and y into 2x+4y yields a result of 4.
Step-by-step explanation:
The student is asked to find the value of 2x+4y given two equations: Equation 1: 3x+5y=9 and Equation 2: x+y=5. The process to find the value of 2x+4y is to solve the two given equations simultaneously.
First, solve Equation 2 for y: y = 5 - x.
Then, substitute this expression for y into Equation 1: 3x + 5(5 - x) = 9.
Simplify and solve for x: 3x + 25 - 5x = 9, resulting in -2x = -16, so x = 8.
Substitute x back into the equation for y: y = 5 - 8, which gives y = -3.
Now, calculate 2x + 4y with the found values of x and y: 2(8) + 4(-3) = 16 - 12 = 4.
Therefore, the value of 2x + 4y is 4.