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

1 Answer
Jul 9, 2015

Answer:

#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