Question

What is the value of 5x+6y if 2x-4y=4 and 4x+6y=8?

Answer 1

Answer:To find the value of 5x + 6y, we need to solve the system of equations:

2x - 4y = 4 (Equation 1)

4x + 6y = 8 (Equation 2)

We can use the method of elimination to solve this system.

First, let's multiply Equation 1 by 2 to make the coefficients of x in both equations the same:

4x - 8y = 8 (Equation 3)

Next, let's add Equation 2 and Equation 3 together:

(4x + 6y) + (4x - 8y) = 8 + 8

8x - 2y = 16 (Equation 4)

Now, let's solve Equation 4 for x:

8x = 16 + 2y

x = (16 + 2y) / 8

x = 2 + (1/4)y

We can substitute this value of x back into Equation 2:

4(2 + (1/4)y) + 6y = 8

8 + 2y + 6y = 8

8y = 0

y = 0

Now, substitute the value of y back into the expression 5x + 6y:

5x + 6(0) = 5x

5x = 5x

The value of 5x + 6y is 5x, which means it depends on the value of x. Since we have expressed x in terms of y as x = 2 + (1/4)y, the value of 5x + 6y can vary depending on the value of y.

Therefore, the value of 5x + 6y is not a specific number but is dependent on the values of x and y in the given system of equations.

Step-by-step explanation:

Answer 2

The value of 5x+6y is 10.

Step-by-step explanation:

To find the value of 5x+6y, we need to solve the system of equations:

2x-4y=4

4x+6y=8

We can solve this system of equations by either substitution or elimination. Let's use elimination:

Multiplying the first equation by 2 and the second equation by -1 gives: 4x-8y=8 and -4x-6y=-8.

Adding these two equations together eliminates the x term: -14y=0. Solving for y gives y=0.

Substituting y=0 back into the first equation, we get 2x=4. Solving for x gives x=2.

Finally, plugging the values of x and y into the expression 5x+6y gives 5(2)+6(0)=10+0=10.