Question

Which of the following is a solution to the system of two equations 4x + y = 51 and 2x – 6y = 6?

Answer 1

The solution to the system of equations given is:

• y = 3
• x = 12

Explanation:

First, we must see our two equations given:

1. 4x + y = 51
2. 2x – 6y = 6

We can use the reduction method, with this, we must eliminate a variable, in this case, de x variable, this can do multiply the equation 2 by (-2) and add the two equations:

• (2x – 6y = 6)*(-2) = (-4x+12y = -12)

3. -4x+12y = -12

Now, we operate the equations 1 and 3:

• (4x + y = 51) + (-4x+12y = -12) = (13y = 39) "The variable x dissapears because 4x - 4x = 0"

4. 13y = 39

We solve the equation 4 and obtain the value for "y":

• 13y = 39
• y = 39/13
• y = 3

With the value of "y," we can replace this value in equation 1 or 2 to obtain the value of "x," in this case, we're gonna use the equation 1:

• 4x + y = 51
• 4x + 3 = 51
• 4x = 51 - 3
• 4x = 48
• x = 48/4
• x = 12

In this form, we know the solution to the system of two equations is: x = 12 and y = 3.