Question

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

Answer 1

`x=2` and `y=-1`

Explanation:

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