Question

What is the solution to the following system of equations?

2 x + 3 y = 6
x + y = 4

The solution of the system of equations is x = ___, y = ___.

Answer 1

x = 6 , y= -2

Explanation:

=1 ( 2x + 3y =6)

2( x+y=4)

2x+3y =6 (1)

2x+2y = 8 (2)

by eq 1 and 2 using elimination method

y = -2

putting y in eq 2

2x + 2(-2)=8

2x -4 =8

2x =8+4

2x=12

x= 6

Answer 2

x = 6 , y = -2

Explanation:

2 x + 3 y = 6 (Equation 1)

x + y = 4 (Equation 2)

Solving by substitution :

(Equation 2) ⇒ y = 4 - x

Substitute y by 4 - x in (equation 1) :

2 x + 3 (4 - x) = 6

Then

2 x + 12 - 3x = 6

Then

12 - x = 6

Then

12 - 6 = x

Then

x = 6

We obtain :

y = 4 - x and x = 6

Then

y = 4 - 6

= -2