How do you solve the following system?: x + 2y = 6 , 2x - 3y = 5

1 Answer

x=4 and y=1

Explanation:

x +2y =6" " " "(1)
2x + 3y =5" " " "(2)

Multiply equation (1) by 3 and equation (2) by 2,

3 xx (x +2y=6) 2 xx (2x -3y=5)#

Therefore,

3x + 6y = 18" " " "(3)
4x - 6y = 10" " " "(4)

Add equation (3) to equation (4)

7x+0=28

Make x the subject of the equation

x=28/7

x=4

Substitute the value of x in equation (1)

x +2y =6

4+2y =6

Collect like terms

2y= 6-4

2y=2

Divide through by 2 to make y the subject of the equation

y=1

Ans:

x=4 and y=1