How do you solve the system of equations 2x + 4y = 12 and y = 3x?

To solve the system of equations, we have the following two equations:

We can use the substitution method since the second equation expresses y in terms of x.

Let’s substitute y in the first equation:

2x + 4(3x) = 12

This simplifies to:

2x + 12x = 12

Combining like terms gives:

14x = 12

Now, let’s solve for x:

x = 12 / 14

x = 6 / 7

Now that we have x, let’s substitute this value back into the second equation to find y:

y = 3(6/7)

y = 18/7

Thus, the solution to the system of equations is:

In summary, the values for x and y that satisfy both equations are:

(x, y) = (6/7, 18/7)

These values represent the point of intersection of the two lines represented by the equations.