# How do you write the the ordered pair that is the solution to the following system of equations: 5x - 2y = 3 and 3x + 4y = 7?

Apr 10, 2017

$\left(1 , 1\right)$

#### Explanation:

The ordered pair is the set of values of $x$ and $y$ which can satisfy a given set of algebraic equations and written as $\left(x , y\right)$ for 2D and as $\left(x , y , z\right)$ for 3D.

For the set of equations;

$5 x - 2 y = 3$

$3 x + 4 y = 7$

We can get the ordered pair by solving them as follows:

Rearranging the 1st equation we have,

$\frac{5 x - 3}{2} = y$

Then, we can substitute this $y$ into the 2nd equation,

$\implies 3 x + 4 \cdot \frac{5 x - 3}{2} = 7$

$\implies 3 x + 10 x - 6 = 7$

$\implies 13 x = 13$

$\implies x = 1$

put the value of $x$ back in the 1st equation to get $y$,

$y = \frac{5 \cdot 1 - 3}{2}$

$\implies y = 1$

Therefore, the solution is written in the ordered pair form as

$\left(x , y\right) = \left(1 , 1\right)$

Apr 10, 2017

The solution is $x = 1 \mathmr{and} y = 1$

As an ordered pair it is $\left(1 , 1\right)$

#### Explanation:

To solve the system of equations you can use several methods.
In this case I would choose elimination of the $y$ terms.

$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots . .} 5 x - 2 y = 3 \text{ } A$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots . .} 3 x + 4 y = 7 \text{ } B$

$A \times 2 : \text{ "10x-4y =6" } C$
$B + C : \text{ "13x" } = 13$

$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots} x = 1$

Now that you know the value for $x$, substitute to find a value for $y$

$3 \left(1\right) + 4 y = 7$
$3 + 4 y = 7$
$4 y = 4$
$y = 1$

The solution is $x = 1 \mathmr{and} y = 1$
As an ordered pair it is $\left(1 , 1\right)$