Answer:
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:
{ equation A in step1 is simplified}.
10. ![p= d+2](https://tex.z-dn.net/?f=p%3D%20d%2B2)
.
Step-by-step explanation:
7. Two equation are given below:
![a-3b=4](https://tex.z-dn.net/?f=a-3b%3D4)
![a=b-2](https://tex.z-dn.net/?f=a%3Db-2)
II eqaution can be write as
![a-b=-2](https://tex.z-dn.net/?f=a-b%3D-2)
Subtracting equation II from equation I then we get
![-2b=6](https://tex.z-dn.net/?f=-2b%3D6)
By division property of equality
![b=\frac{6}{-2}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B6%7D%7B-2%7D)
By simplification we get
![b=-3](https://tex.z-dn.net/?f=b%3D-3)
Substitute the value of b in equation I then we get
![a-3(-3)=4](https://tex.z-dn.net/?f=a-3%28-3%29%3D4)
![a+9=4](https://tex.z-dn.net/?f=a%2B9%3D4)
![a=4-9](https://tex.z-dn.net/?f=a%3D4-9)
![a=-5](https://tex.z-dn.net/?f=a%3D-5)
Hence, the solution of the set of equation is (-5,-3).
8. Equation A: ![x+z=6](https://tex.z-dn.net/?f=x%2Bz%3D6)
Equation B: ![2x+4z=1](https://tex.z-dn.net/?f=2x%2B4z%3D1)
Equation A is multiplied by -4 then we get
Equation A:![-4x-4z=-24](https://tex.z-dn.net/?f=-4x-4z%3D-24)
Adding both equation A and B then we get
![-2x=-23](https://tex.z-dn.net/?f=-2x%3D-23)
Answer: Multiply equation A by -4 to eliminate the z-term.
9.Equation A: ![y=4-2z](https://tex.z-dn.net/?f=y%3D4-2z)
Equation B:![4y=2-4z](https://tex.z-dn.net/?f=4y%3D2-4z)
Step1 :![-4(y)=-4(4-2z)](https://tex.z-dn.net/?f=-4%28y%29%3D-4%284-2z%29)
Equation A is multiplied by -4
[equation B]
Step 2: ![-4y=-16+8z](https://tex.z-dn.net/?f=-4y%3D-16%2B8z)
[equation B]
Equation A in step1 s simplified .
Step3: ![0= -14+4z](https://tex.z-dn.net/?f=0%3D%20-14%2B4z)
Equations in step 2 are added.
Step 4: ![4z=14](https://tex.z-dn.net/?f=4z%3D14)
Step5: ![z=\frac{7}{2}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B7%7D%7B2%7D)
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](https://tex.z-dn.net/?f=p%3Dd%2B2)
Variable p is also 1 less than variable d.
Then the algebraic expression
![p=d-1](https://tex.z-dn.net/?f=p%3Dd-1)
Hence, ![p=d+2](https://tex.z-dn.net/?f=p%3Dd%2B2)
![p=d-1](https://tex.z-dn.net/?f=p%3Dd-1)