# How do you solve the system using the elimination method for 3x+y=5 and x-2y=4?

Jul 9, 2015

$x = 2$ and $y = - 1$

#### Explanation:

Hi there,

Here we will use elimination method to solve the given system of an equation.

We have,
$3 x + y = 5$................equation 1
$x - 2 y = 4$..................equation 2

Note: here we have unequal coefficient for both x and y. So we will first make coefficient of either x or y equal.

Here we well make coefficient of y equal by multiplying equation 1 by 2, we get

$6 x + 2 y = 10$..........equation 3

Now, we have coefficient of y equal with opposite sign, hence it can be eliminated on addition.

Adding equation 2 and 3, we get
$x - 2 y = 4$
$6 x + 2 y = 10$
$- - - - -$
$7 x = 14$

Now divide both side by 7, we get
or, $x = \frac{14}{7} = 2$

Plug the value of x= 2 in equation 1, we get
$3 X 2 + y = 5$
or, $6 + y = 5$
Subtract 6 on both side, we get
or, $y = 5 - 6$
or. $y = - 1$

Therefore, the final answer is $x = 2$ and $y = - 1$

To check the answer, plug $x = 2$ and $y = - 1$ in above equation and check weather it satisfies or not.

Thanks