Solve the system -2x-y=-9 5x-2y=18

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hala718's profile pic

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

Posted on

-2x - y = -9.............(1)

5x - 2y = 18..............(2)

We will use the substitution method to solve the system.

First, we will rewrite equation (1).

==> -2x - y = -9

==> y = -2x + 9 .................(3)

Now we will substitute (3) into (2).

==> 5x - 2y = 18

==> 5x - 2 ( -2x + 9) = 18

==> 5x + 4x - 18 = 18

==> 9x = 36

Now we will divide by 9.

==> x= 4

Now to find y, we will substitute into equation (3);

==> y= -2x + 9

==> y= -2(4) + 9

           = -8 + 9 = 1

==> y= 1

Then, the solution is the pair ( 4,1)

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to solve

-2x-y=-9 ...(1)

5x-2y=18 ...(2)

(2) - 2*(1)

=> 5x - 2y + 4x + 2y = 18 + 18

=> 9x = 36

=> x = 4

Substitute x = 4 in (1)

-2x-y=-9

=> y = 9 - 2*4

=> y = 9 - 8

=> y = 1

Therefore x is 4 and y is 1.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll solve the system using substitution. We'll change the first equation.

-2x-y=-9

We'll add 2x:

-y = 2x - 9

We'll multiply by -1:

y = -2x + 9 (1)

5x-2y=18 (2)

We'll substitute (1) in (2):

5x - 2(-2x + 9) = 18

We'll remove the brackets:

5x + 4x - 18 = 18

We'll combine like terms:

9x = 18 + 18

x = 2*18/9

x = 4

We'll substitute x = 4 in (1):

y = -2*4 + 9

y = 9 - 8

y = 1

The solution of the system is: {4 ; 1}.

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