What is the solution to the system of equations? use any method. {3x+y=32x+y=7 {2x+y=7

x = 12  and  y = 1

Explanation:

Given equations are:

(1)  1 3 x − y = 3

(2) 2 x + y = 25

Multiply (1) by 3 to eliminate the fractional part,

(1)  x − 3 y = 9  ⇒ x = 9 + 3 y

let this be equation (3)

Now substitute this value of  

x

from (3) in equation (2),

(2)  2 ( 9 + 3 y ) + y = 25  ⇒ 18 + 6 y + y = 25  ⇒ 7 y = 25 − 18  ⇒ y = 7 7

Therefore,

y = 1

Substituting this value of  

y

in equation (3),

x = 9 + 3 × 1  

x = 9 + 3

Therefore,

x = 12

So we have the values of  

x  and  y  as,

x = 12

and  

y = 1

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