How do you solve the following system 4x + 2y = 3 and 3x + y = 6?

To solve the system of equations 4x + 2y = 3 and 3x + y = 6, we can use the substitution or elimination method. Here, I’ll show you how to solve it using the elimination method.

1. First, arrange the equations:

Equation 1: 4x + 2y = 3
Equation 2: 3x + y = 6

2. Next, we want to eliminate one variable. We can do this by multiplying Equation 2 by 2 to match the coefficient of y in Equation 1. This gives us:

Equation 2: 2(3x + y) = 2(6)
=> 6x + 2y = 12

3. Now we have:

Equation 1: 4x + 2y = 3
Equation 3: 6x + 2y = 12

4. We can subtract Equation 1 from Equation 3 to eliminate y:

(6x + 2y) - (4x + 2y) = 12 - 3
=> 2x = 9

5. Solve for x:

x = 9/2

6. Now that we have the value of x, we can substitute it back into one of the original equations to find y. We’ll use Equation 2:

3(9/2) + y = 6
=> 27/2 + y = 6
=> y = 6 - 27/2
=> y = 12/2 - 27/2
=> y = -15/2

7. Therefore, the solution to the system of equations is:

(x, y) = (9/2, -15/2)

This means that when you plot the lines represented by these equations, they will intersect at the point (4.5, -7.5).