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

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Answer 1 · 2015-07-09T12:33:53

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

Hi there,

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

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

$6x+2y=10$ ..........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
$x-2y = 4$
$6x+2y=10$
$-----$
$7x = 14$

Now divide both side by 7, we get
or, $x = 14/7 = 2$

Plug the value of x= 2 in equation 1, we get
$3X2+y=5$
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