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

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.

.

Step-by-step explanation:

7. Two equation are given below:

II eqaution can be write as

Subtracting equation II from  equation I then we get

By division property of equality

By simplification we get

Substitute the value of b in equation I then we get

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

8. Equation A:

Equation B:

Equation A is multiplied by -4 then we get

Equation A:

Adding both equation A and B then we get

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

9.Equation A:

Equation B:

Step1 :

Equation A is multiplied by -4

[equation B]

Step 2:

[equation B]

Equation A in step1 s simplified .

Step3:

Equations in step 2 are added.

Step 4:

Step5:

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

Variable p is also 1 less than variable d.

Then the algebraic expression

Hence,

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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