Solve the system using the elimination method: 3x+4y=26 x-2y=-8

2 Answers

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the equation:

3x+4y = 26...........(1)

x - 2y = -8 ............(2)

First we will multiply (2) by 2 :

==> 2x - 4y = -16...........(3)

Now we will add (1) and (3)

==> 5x = 10

==> x = 2

==> Now we will substitute x=2 into (2) to find y.

==> x - 2y = -8

==> 2 - 2y = -8

==> -2y = -10

==> y= 5

Then, the solution to the system is the pair ( 2, 5)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Let's try to eliminate the other variable, namely the variable x. For this reason, we'll multiply the second equation by -3:

3x + 4y = 26

-3x + 6y = 24

Now, we'll add equations above:

3x + 4y - 3x + 6y = 26 + 24

We'll combine and eliminate like terms:

10y = 50

We'll divide by 10:

y = 5

We'll substitute y in the 2nd equation:

x - 10 = -8

We'll add 10:

x = 10 - 8

x = 2

The solution of the system is (2 ; 5).