Question

What is the solution to this system of equations?

3x + y = 17
x + 2y = 49
A.
It has no solution.
B.
It has infinite solutions.
C.
It has a single solution: x = 15, y = 17.
D.
It has a single solution: x = -3, y = 26.
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Answer 1

Choice D is correct answer.

Explanation:

We have given a system of equations.

3x + y = 17 eq(1)

x + 2y = 49 eq(2)

We have to find the solution of given system.

Multiplying by 2 to both sides of eq(1), we have

6x+2y = 34 eq(3)

Subtracting eq(2) from eq(3), we have

6x+2y-(x+2y) = 34-49

6x+2y-x-2y = -15

5x = -15

x = -3

Putting the value of x in eq(2), we have

(-3)+2y = 49

2y = 49+3

2y = 52

y = 26

Hence, it has a single solution: x = -3, y = 26.

Answer 2

D. It has a single solution: x = -3, y = 26.

Explanation:

The given system is

`3x+y=17...(1)`

and

`x+2y=49...(2)`.

Make x the subject in equation (2).

`x=49-2y....(3)`.

Put equation (3) into equation (1).

`3(49-2y)+y=17`

`147-6y+y=17`

`-6y+y=17-147`

`-5y=-130`

`y=26`

`x=49-2(26)=-3`

It has a single solution: x = -3, y = 26.