# How do you find the solution of the system of equations 3x+4y=10 and x-y=1?

Jun 7, 2018

$x = 2$ and $y = 1$

#### Explanation:

For such a simple system, you can use substitution: $x = y + 1$ from the second equation. Substitute this value of $x$ in the first equation to the effect that
$3 \left(y + 1\right) + 4 y = 10$. this simplifies to $7 y = 7$, that is $y = 1$.

Substitute back in the second equation to get $x = y + 1 = 1 + 1 = 2$.

Jun 7, 2018

$x = 2 , y = 1$

#### Explanation:

The key insight here is that for the second equation, we can easily solve for a variable in term of the other variable.

Let's just add $y$ to both sides to solve for $x$ in terms of $y$. We get

$\textcolor{b l u e}{x = y + 1}$

We can plug this value of $x$ into the first equation in the system. We get

$3 \left(y + 1\right) + 4 y = 10$

Distributing the $3$ to both terms in the parenthesis, we get

$3 y + 3 + 4 y = 10$

Combining like terms, we now have

$7 y + 3 = 10$

Subtracting $3$ from both sides, we get

$7 y = 7$

Dividing both sides by $7$, we find that

$\textcolor{red}{y = 1}$

We can plug this value into the blue expression to get

$x = 1 + 1$

$\textcolor{red}{\implies x = 2}$

Hope this helps!