# How do you solve y+6=2x & 4x-10y=4?

May 25, 2017

$x = \frac{7}{2}$ and $y = 1$

#### Explanation:

Strategy: Solve for $y$ in terms of $x$. Plug in that $y$ equation into the other equation to solve for $x$. With the solution for $x$, you can back track and find the solution for $y$.

Step 1. Solve for $y$ in terms of $x$.
$y + 6 = 2 x$ given
$y = 2 x - 6$ subtract 6 from both sides

Step 2. Plug this $y$ equation into the other equation.
$4 x - 10 \textcolor{red}{y} = 4$ ; given
$4 x - 10 \left(\textcolor{red}{2 x - 6}\right) = 4$ ; replace variable $y$ with $2 x - 6$
$4 x - 20 x + 60 = 4$ ; distribute $- 10$ through
$- 16 x = - 56$ ; combine $x$ terms and subtract $60$ both sides
$x = \frac{7}{2}$ ; divide both sides by $- 16 \mathmr{and} red u c e$

Step 3. Plug this solution back into the equation of step 1.
$y = 2 \textcolor{red}{x} - 6$ ; final part of step 1
$y = 2 \left(\textcolor{red}{\frac{7}{2}}\right) - 6$ ; solution for $x$ in step 2
$y = 7 - 6 = 1$

So your solution is $x = \frac{7}{2}$ and $y = 1$

May 25, 2017

$\left(\frac{7}{2} , 1\right)$

#### Explanation:

$\textcolor{red}{y} + 6 = 2 x \to \left(1\right)$

$4 x - 10 \textcolor{red}{y} = 4 \to \left(2\right)$

$\text{note that in " (1)" y can be expressed in terms of x}$

$\Rightarrow \textcolor{red}{y} = 2 x - 6 \to \left(3\right)$

$\text{substitute into } \left(2\right)$

$\Rightarrow 4 x - 10 \left(2 x - 6\right) = 4$

$\Rightarrow 4 x - 20 x + 60 = 4 \leftarrow \text{ distributing}$

$\Rightarrow - 16 x + 60 = 4 \leftarrow \text{ simplifying left side}$

$\text{subtract 60 from both sides}$

$- 16 x \cancel{+ 60} \cancel{- 60} = 4 - 60$

$\Rightarrow - 16 x = - 56$

$\text{divide both sides by - 16}$

$\frac{\cancel{- 16} x}{\cancel{- 16}} = \frac{- 56}{- 16}$

$\Rightarrow x = \frac{56}{16} = \frac{7}{2}$

$\text{substitute this value in " (3)" and evaluate for y}$

$y = \left(2 \times \frac{7}{2}\right) - 6 = 7 - 6 = 1$

$\left(\frac{7}{2} , 1\right) \text{ is the point of intersection of the 2 equations}$
graph{(y-2x+6)(y-2/5x+2/5)=0 [-10, 10, -5, 5]}