x+5=12

Question 1

Carly and Janiya put some money into their money boxes every week. The amounts of money (y), in dollars, in their money boxes after certain amounts of time (x), in weeks, are shown by the equations below:

Carly

y = 60x + 40

Janiya

y = 50x + 80

After how many weeks will Carly and Janiya have the same amount of money in their money boxes and what will that amount be?

5 weeks, $280

5 weeks, $340

4 weeks, $280

4 weeks, $340

Question 2

A system of equations is shown below:

y = 8x − 2

y = 9x − 7

What is the solution to the system of equations?

(−5, 38)

(−5, −38)

(5, 38)

(5, −38)

Question 3

Two equations are given below:

m + 3n = 10

m = n − 2

What is the solution to the set of equations in the form (m, n)?

(1, 3)

(2, 4)

(0, 2)

(4, 6)

Question 4

The work of a student to solve a set of equations is shown:

Equation 1: m = 8 + 2n

Equation 2: 3m = 4 + 4n

Step 1:

−3(m) =

−3(8 + 2n)

[Equation 1 is multiplied by −3.]

3m =

4 + 4n

[Equation 2]

Step 2:

−3m =

−24 − 6n

[Equation 1 in Step 1 is simplified.]

3m =

4 + 4n

[Equation 2]

Step 3:

−3m + 3m =

−24 − 6n + 4n

[Equations in Step 2 are added.]

Step 4:

0 =

−24 − 2n

Step 5:

n =

−12

In which step did the student first make an error?

Step 4

Step 3

Step 2

Step 1

Question 5

A student is trying to solve the system of two equations given below:

Equation P: y + z = 6

Equation Q: 8y + 7z = 1

Which of the following is a possible step used in eliminating the y-term?

(y + z = 6) ⋅ −8

(y + z = 6) ⋅ 7

(8y + 7z = 1) ⋅ 7

(8y + 7z = 1) ⋅ 8

Question 6

Line A is represented by the equation given below:

x + y = 4

What is most likely the equation for line B, so that the set of equations has infinitely many solutions?

4x + 4y = 4

4x + y = 4

2x + 2y = 8

x + y = 8

Report

by EvilEvie 10.05.2018

Answers

SamanthaBees · Beginner

Know the answer? Add it here!

MsEHolt Brainly Teacher

#1) 4 weeks, $280

#2) (5, 38)

#3) (1, 3)

#4) Step 3

#5) (y+z=6)*-8

#6) 2x+2y=8

Explanation

#1) Setting them equal,

60x+40=50x+80

Subtract 50x from both sides:

60x+40-50x=50x+80-50x

10x+40=80

Subtract 40 from both sides:

10x+40-40=80-40

10x=40

Divide both sides by 10:

10x/10 = 40/10

x=4

Plugging this in to one of our equations,

60(4)+40=240+40=280

#2) Setting the equations equal to one another,

8x-2=9x-7

Subtract 8x from both sides:

8x-2-8x=9x-7-8x

-2=x-7

Add 7 to both sides:

-2+7=x-7+7

5=x

Plugging this in to the first equation,

8(5)-2=y

40-2=y

38=y

#3) Substituting our value from the second equation into the first one,

n-2+3n=10

Combining like terms,

4n-2=10

Add 2 to both sides:

4n-2+2=10+2

4n=12

Divide both sides by 4:

4n/4 = 12/4

n=3

Substitute this into the second equation:

m=3-2=1

#4) The mistake was made on Step 3; the 4 was left off when the equations were added.

#5) To eliminate y, we want the coefficients to be the same. To accomplish this, we will multiply the first equation by -8.

#6) In order to have infinitely many solutions, we want each coefficient as well as the constant to be a multiple of our equation. Multiplying the equation by 2, we get 2x+2y=8.

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,

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,

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 2he didn't distribute correctly <==

10. p = d + 2 : p = d - 1 <==

-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 2he didn't distribute correctly <==

10. p = d + 2 : p = d - 1 <==

#1) 4 weeks, $280

#2) (5, 38)

#3) (1, 3)

#4) Step 3

#5) (y+z=6)*-8

#6) 2x+2y=8

Explanation

#1) Setting them equal,

60x+40=50x+80

Subtract 50x from both sides:

60x+40-50x=50x+80-50x

10x+40=80

Subtract 40 from both sides:

10x+40-40=80-40

10x=40

Divide both sides by 10:

10x/10 = 40/10

x=4

Plugging this in to one of our equations,

60(4)+40=240+40=280

#2) Setting the equations equal to one another,

8x-2=9x-7

Subtract 8x from both sides:

8x-2-8x=9x-7-8x

-2=x-7

Add 7 to both sides:

-2+7=x-7+7

5=x

Plugging this in to the first equation,

8(5)-2=y

40-2=y

38=y

#3) Substituting our value from the second equation into the first one,

n-2+3n=10

Combining like terms,

4n-2=10

Add 2 to both sides:

4n-2+2=10+2

4n=12

Divide both sides by 4:

4n/4 = 12/4

n=3

Substitute this into the second equation:

m=3-2=1

#4) The mistake was made on Step 3; the 4 was left off when the equations were added.

#5) To eliminate y, we want the coefficients to be the same. To accomplish this, we will multiply the first equation by -8.

#6) In order to have infinitely many solutions, we want each coefficient as well as the constant to be a multiple of our equation. Multiplying the equation by 2, we get 2x+2y=8.

#2) (5, 38)

#3) (1, 3)

#4) Step 3

#5) (y+z=6)*-8

#6) 2x+2y=8

Explanation

#1) Setting them equal,

60x+40=50x+80

Subtract 50x from both sides:

60x+40-50x=50x+80-50x

10x+40=80

Subtract 40 from both sides:

10x+40-40=80-40

10x=40

Divide both sides by 10:

10x/10 = 40/10

x=4

Plugging this in to one of our equations,

60(4)+40=240+40=280

#2) Setting the equations equal to one another,

8x-2=9x-7

Subtract 8x from both sides:

8x-2-8x=9x-7-8x

-2=x-7

Add 7 to both sides:

-2+7=x-7+7

5=x

Plugging this in to the first equation,

8(5)-2=y

40-2=y

38=y

#3) Substituting our value from the second equation into the first one,

n-2+3n=10

Combining like terms,

4n-2=10

Add 2 to both sides:

4n-2+2=10+2

4n=12

Divide both sides by 4:

4n/4 = 12/4

n=3

Substitute this into the second equation:

m=3-2=1

#4) The mistake was made on Step 3; the 4 was left off when the equations were added.

#5) To eliminate y, we want the coefficients to be the same. To accomplish this, we will multiply the first equation by -8.

#6) In order to have infinitely many solutions, we want each coefficient as well as the constant to be a multiple of our equation. Multiplying the equation by 2, we get 2x+2y=8.

The first thing you do is subtract negative 5 on both side because we want to get x by itself.

Then we subtract 12 -5 which get us 7.

So, the solution is x=7.

And that how you solve the equation.

Then we subtract 12 -5 which get us 7.

So, the solution is x=7.

And that how you solve the equation.

Then we subtract 12 -5 which get us 7.

So, the solution is x=7.

And that how you solve the equation.

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