# How do you solve the system of equations 2x + 6y = 14 and 4x = 16?

May 12, 2017

Reduce each equation then substitute the second equation into the first equation. Answer: $\left(4 , 1\right)$

#### Explanation:

Original equation: Given $2 x + 6 y = 14$ and $4 x = 16$, solve for $\left(x , y\right)$

We can solve this system of equations by using substitution. First, we can divide the first equation by $2$ and the second equation by $4$:
$x + 3 y = 7$
$x = 4$

Now, we simply substitute the second equation, $x = 4$, into the first equation:
$4 + 3 y = 7$
We can subtract $4$ from both sides to isolate the $3 y$:
$4 + 3 y - 4 = 7 - 4$
$3 y = 3$
Now, we divide both sides by $3$ to solve for $y$:
$y = 1$

Therefore, our solution is the coordinate point $\left(4 , 1\right)$