Question

Use the substitution method to solve the system of equations. Choose the correct ordered pair.

Answer 1

Answer:  The correct option is (A) (2, 6).

Step-by-step explanation:  We are given to use the substitution method to solve the following system of equations :

$x+2y=14~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x+4~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Substituting the value of y from equation (ii) in equation (i), we get

$x+2y=14\\\\\Rightarrow x+2(x+4)=14\\\\\Rightarrow x+2x+8=14\\\\\Rightarrow 3x=14-8\\\\\Rightarrow 3x=6\\\\\Rightarrow x=\dfrac{6}{3}\\\\\Rightarrow x=2.$

Again, from equation (ii), we get

$y=x+4=2+4=6.$

Thus, the required solution of the given system of equations is (x, y) = (2, 6).

Option (A) is CORRECT.

Answer 2

Answer:

x = 2

Step-by-step explanation:

According to the second equation, y = x + 4.  Substitute x + 4 for y in the first equation, obtaining:

x + 2(x + 4) = 14, or:

x + 2x + 8 = 14

Combining the x terms, we get:

3x + 8 = 14

Combining the constant terms, we get:

3x = 6

Therefore, x = 6/3 = 2