Question

7.

Two equations are given below:

a – 3b = 4
a = b – 2

What is the solution to the set of equations in the form (a, b)? (5 points)



(–2, –2)
(–3, –1)
(–9, –7)
(–5, –3)
8.
A student is trying to solve the set of two equations given below:

Equation A: x + z = 6
Equation B: 2x + 4z = 1

Which of the following is a possible step used in eliminating the z-term? (5 points)



Multiply equation B by 4.
Multiply equation A by 2.
Multiply equation A by –4.
Multiply equation B by 2.
9.
The work of a student to solve a set of equations is shown:

Equation A: y = 4 – 2z
Equation B: 4y = 2 – 4z

Step 1: –4(y) = –4(4 – 2z) [Equation A is multiplied by –4.]
4y = 2 – 4z [Equation B]
Step 2: –4y = 4 – 2z [Equation A in Step 1 is simplified.]
4y = 2 – 4z [Equation B]
Step 3: 0 = 6 – 6z [Equations in Step 2 are added.]
Step 4: 6z = 6
Step 5: z = 1


In which step did the student first make an error? (5 points)



Step 1
Step 3
Step 4
Step 2
10.
Variable p is 2 more than variable d. Variable p is also 1 less than variable d. Which pair of equations best models the relationship between p and d? (5 points)



p = d + 2
p = d – 1
p = d – 2
p = d + 1
d = 2p
d = 2p – 1
d = 2p
d = 2p + 1

Answer 1

7. b - 2 - 3b = 4
-2b = 6
b = -3
a = -5
solution is (-5,-3) <==
8. multiply A by -4...this eliminates the z's when added <==
9. first error...step 2....he didn't distribute correctly <==
10. p = d + 2 : p = d - 1 <==

Answer 2

7.The solution to the set of equation in the form (-5,-3).

8.Multiply equation A by -4 used to eliminate the z- term.

9.Step 2:
`-4y=-16+8z` { equation A in step1 is simplified}.

10.
`p= d+2`

`p=d-1`.

Explanation:

7. Two equation are given below:

`a-3b=4`

`a=b-2`

II eqaution can be write as

`a-b=-2`

Subtracting equation II from equation I then we get

`-2b=6`

By division property of equality

`b=(6)/(-2)`

By simplification we get

`b=-3`

Substitute the value of b in equation I then we get

`a-3(-3)=4`

`a+9=4`

`a=4-9`

`a=-5`

Hence, the solution of the set of equation is (-5,-3).

8. Equation A:
`x+z=6`

Equation B:
`2x+4z=1`

Equation A is multiplied by -4 then we get

Equation A:
`-4x-4z=-24`

Adding both equation A and B then we get

`-2x=-23`

Answer: Multiply equation A by -4 to eliminate the z-term.

9.Equation A:
`y=4-2z`

Equation B:
`4y=2-4z`

Step1 :
`-4(y)=-4(4-2z)`

Equation A is multiplied by -4

`4y=2-4z` [equation B]

Step 2:
`-4y=-16+8z`

`4y=2-4z` [equation B]

Equation A in step1 s simplified .

Step3:
`0= -14+4z`

Equations in step 2 are added.

Step 4:
`4z=14`

Step5:
`z=(7)/(2)`

Hence, in step 2 student did make first an error.

10. Given

Variable p is more than variable d

We can write in algebraic expression

`p=d+2`

Variable p is also 1 less than variable d.

Then the algebraic expression

`p=d-1`

Hence,
`p=d+2`

`p=d-1`