Question

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

Answer 1

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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Answer 2

Answer: (-4, 15)

Step-by-step explanation: When we graph these equations, the lines intersect at (-4, 15), hence being the answer.