Solution to the System of Equations

We are given the two equations:

1. y = 3x + 10
2. 2x + y = 4

To find the solution, we will use the substitution method:

Step 1: Substitute y in the second equation

We can substitute the expression of y from the first equation into the second equation:

2x + (3x + 10) = 4

This simplifies to:

2x + 3x + 10 = 4

Combine like terms:

5x + 10 = 4

Step 2: Solve for x

Next, we isolate x:

5x = 4 - 10

5x = -6

x = -\frac{6}{5}

Step 3: Substitute x back to find y

Now that we have the value of x, we substitute it back into the first equation to find y:

y = 3(-\frac{6}{5}) + 10

Calculating this gives:

y = -\frac{18}{5} + 10

y = -\frac{18}{5} + \frac{50}{5}

y = \frac{32}{5}

Final Solution

The solution to the system of equations is:

(x, y) = \left(-\frac{6}{5}, \frac{32}{5}\right)