# Question #2077b

May 16, 2017

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

#### Explanation:

Solve:
$2 x + 3 y = 10$
$5 x + 2 y = 19.5$

We can solve this system of equations by elimination.
First, we need to multiply the first equation by $5$ and the second equation by $2$ to make the $x$ coefficient same for both equations:
$5 \left(2 x + 3 y = 10\right)$
$10 x + 15 y = 50$

$2 \left(5 x + 2 y = 19.5\right)$
$10 x + 4 y = 39$

Since the $x$ coefficient for both equations is now $10$, we can subtract the second equation from the first equation and simplify:
$10 x + 15 y - \left(10 x + 4 y\right) = 50 - 39$
$10 x + 15 y - 10 x - 4 y = 11$
$11 y = 11$
$y = 1$

Now, we can substitute this $y$ value into one of the original equations and solve for $x$, we'll use the first one:
$2 x + 3 \left(1\right) = 10$
$2 x + 3 = 10$
$2 x = 7$
$x = \frac{7}{2}$

Therefore, our answer as a coordinate is $\left(\frac{7}{2} , 1\right)$