Question

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

x+2y=12
-x=-y-6

a. (6,0)
b. (7,1)
c. (8,2)
d. (9,3)

Answer 1

c

Explanation:

Solution by substitution method

x+2y=12

and -x=-y-6

∴-x+y=-6

x-y=6

Suppose,

x+2y=12→(1)

and x-y=6→(2)

Taking equation (1), we have

x+2y=12

⇒x=-2y+12→(3)

Putting x=-2y+12 in equation (2), we get

x-y=6

(-2y+12)-y=6

⇒-2y+12-y=6

⇒-3y+12=6

⇒-3y=6-12

⇒-3y=-6

⇒y=2→(4)

Now, Putting y=2 in equation (3), we get

x=-2y+12

⇒x=-2(2)+12

⇒x=-4+12

⇒x=8

∴x=8 and y=2

Answer 2

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Answer:

c. (8, 2)

Explanation:

Multiplying the second equation by -1 gives an expression for x that can be substituted into the first equation.

x = y +6

(y +6) +2y = 12

3y = 6 . . . . . . . subtract 6

y = 2 . . . . . . . . eliminates all choices except C

Using the expression for x, we can find the complete solution:

x = y +6 = 2 +6 = 8

(x, y) = (8, 2) . . . . matches choice C