Question

What is the solution of the system?

Use either the substitution method or the elimination method.

4x + 2y = 10
x − y = 13

A. (6, −7)

B. There is no solution.

C. (−7.5, 2)

D. (3.5, −1)

Answer 1

The given system is:

4x + 2y = 10.................Equation 1

x − y = 13......................Equation 2

Let us use the method of substitution to solve this problem.

To begin with, let us isolate x in the (Equation 2) as:

x=13+y......................Equation 3

Let us now plug in this value of x into (Equation 1). That will give us:

4x+2y=4(13+y)+2y=10

52+4y+2y=10

52+6y=10

Subtracting 52 from both sides, we get

6y=-42

`\therefore y=(-42)/(6)=-7`

Now, inorder to find x, we will plug in y=-7 in (Equation 3):

x=13+y=13-7=6

Thus, Option A with the ordered pair (6,-7) is the correct option.