# Solve the system 7x + 2y = 12                               x - 3y = 5

Asked on by lipiciuc

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

Posted on

7x + 2y = 12 ....(1)

x-3y = 5 ............(2)

Using the substotitution method
rewrite (2):

==> x= 3y + 5

Now substotitute in (1):

7x + 2y = 12

7(3y+5) + 2y = 12

21y + 35 = 2y = 12

23y = -23

==> y= -23/23= 1

==> y= 1

Now to calculate x:

x= 3y + 5

= 3(1) +5 = 8

==> x= 8

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll use substitution method for solving the system. We'll note the equations of the system as:

7x + 2y = 12 (1)

x - 3y = 5  (2)

We'll isolate x in the second eq.:

x = 3y+5 (3)

We'll substitute (3) into (1):

7(3y+5) + 2y = 12

We'll remove the brackets:

21y + 35 + 2y - 12 = 0

We'll combine like terms:

23y + 23 = 0

We'll factorize:

23 (y+1) = 0

We'll divide by 23:

y+1 = 0

y = -1

We'll substitute y in (3):

x = 3y+5

x = -3 + 5

x = 2

The solution of the system is {(2,-1)}.

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