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Can someone please help with the following two systems of equations? Thanks!

 

2x+y=10

x-y=2

 

9(2x+2)-y=21

x-y=-48

 Oct 20, 2019

Best Answer 

 #1
avatar+435 
+7

There are 2 ways to do each of them. 

 

For the 1st one lets start with substitution.

 

2x+y=10

x-y=2

 

SUBSTITUTION

 

Step: Solve2x+y=10for y:

2x+y=10

2x+y+−2x=10+−2x(Add -2x to both sides)

y=−2x+10

 

Step: Substitute−2x+10foryinx−y=2:

x−y=2

x−(−2x+10)=2

3x−10=2(Simplify both sides of the equation)

3x−10+10=2+10(Add 10 to both sides)

3x=12

3x

3

=

12

3

(Divide both sides by 3)

x=4

 

Step: Substitute4forx in y=−2x+10:

y=−2x+10

y=(−2)(4)+10

y=2(Simplify both sides of the equation)

 

Answer:

x=4 and y=2

 

Now let's do Elimination

 

ELIMINATION

 

2x+y=10

x−y=2

Add these equations to eliminate y:

3x=12

Then solve3x=12for x:

3x=12

3x

3

=

12

3

(Divide both sides by 3)

x=4

 

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

2x+y=10

Substitute4forxin2x+y=10:

(2)(4)+y=10

y+8=10(Simplify both sides of the equation)

y+8+−8=10+−8(Add -8 to both sides)

y=2

 

NUMBER 2

 

Substitution

 

18x−y+18=21;x−y=−48

Step: Solve18x−y+18=21for y:

18x−y+18+−18=21+−18(Add -18 to both sides)

18x−y=3

18x−y+−18x=3+−18x(Add -18x to both sides)

−y=−18x+3

−y

−1

=

−18x+3

−1

(Divide both sides by -1)

y=18x−3

Step: Substitute18x−3foryinx−y=−48:

x−y=−48

x−(18x−3)=−48

−17x+3=−48(Simplify both sides of the equation)

−17x+3+−3=−48+−3(Add -3 to both sides)

−17x=−51

−17x

−17

=

−51

−17

(Divide both sides by -17)

x=3

Step: Substitute3forxiny=18x−3:

y=18x−3

y=(18)(3)−3

y=51(Simplify both sides of the equation)

 

Elimination

 

Multiply the second equation by -1, then add the equations together.

(18x−y+18=21)

−1(x−y=−48)

Becomes:

18x−y+18=21

−x+y=48

Add these equations to eliminate y:

17x+18=69

Then solve17x+18=69for x:

17x+18+−18=69+−18(Add -18 to both sides)

17x=51

17x

17

=

51

17

(Divide both sides by 17)

x=3

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

18x−y+18=21

Substitute3forxin18x−y+18=21:

(18)(3)−y+18=21

−y+72=21(Simplify both sides of the equation)

−y+72+−72=21+−72(Add -72 to both sides)

−y=−51

−y

−1

=

−51

−1

(Divide both sides by -1)

y=51

 

wink

SVS


 

 Oct 20, 2019
edited by SVS2652  Oct 20, 2019
 #1
avatar+435 
+7
Best Answer

There are 2 ways to do each of them. 

 

For the 1st one lets start with substitution.

 

2x+y=10

x-y=2

 

SUBSTITUTION

 

Step: Solve2x+y=10for y:

2x+y=10

2x+y+−2x=10+−2x(Add -2x to both sides)

y=−2x+10

 

Step: Substitute−2x+10foryinx−y=2:

x−y=2

x−(−2x+10)=2

3x−10=2(Simplify both sides of the equation)

3x−10+10=2+10(Add 10 to both sides)

3x=12

3x

3

=

12

3

(Divide both sides by 3)

x=4

 

Step: Substitute4forx in y=−2x+10:

y=−2x+10

y=(−2)(4)+10

y=2(Simplify both sides of the equation)

 

Answer:

x=4 and y=2

 

Now let's do Elimination

 

ELIMINATION

 

2x+y=10

x−y=2

Add these equations to eliminate y:

3x=12

Then solve3x=12for x:

3x=12

3x

3

=

12

3

(Divide both sides by 3)

x=4

 

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

2x+y=10

Substitute4forxin2x+y=10:

(2)(4)+y=10

y+8=10(Simplify both sides of the equation)

y+8+−8=10+−8(Add -8 to both sides)

y=2

 

NUMBER 2

 

Substitution

 

18x−y+18=21;x−y=−48

Step: Solve18x−y+18=21for y:

18x−y+18+−18=21+−18(Add -18 to both sides)

18x−y=3

18x−y+−18x=3+−18x(Add -18x to both sides)

−y=−18x+3

−y

−1

=

−18x+3

−1

(Divide both sides by -1)

y=18x−3

Step: Substitute18x−3foryinx−y=−48:

x−y=−48

x−(18x−3)=−48

−17x+3=−48(Simplify both sides of the equation)

−17x+3+−3=−48+−3(Add -3 to both sides)

−17x=−51

−17x

−17

=

−51

−17

(Divide both sides by -17)

x=3

Step: Substitute3forxiny=18x−3:

y=18x−3

y=(18)(3)−3

y=51(Simplify both sides of the equation)

 

Elimination

 

Multiply the second equation by -1, then add the equations together.

(18x−y+18=21)

−1(x−y=−48)

Becomes:

18x−y+18=21

−x+y=48

Add these equations to eliminate y:

17x+18=69

Then solve17x+18=69for x:

17x+18+−18=69+−18(Add -18 to both sides)

17x=51

17x

17

=

51

17

(Divide both sides by 17)

x=3

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

18x−y+18=21

Substitute3forxin18x−y+18=21:

(18)(3)−y+18=21

−y+72=21(Simplify both sides of the equation)

−y+72+−72=21+−72(Add -72 to both sides)

−y=−51

−y

−1

=

−51

−1

(Divide both sides by -1)

y=51

 

wink

SVS


 

SVS2652 Oct 20, 2019
edited by SVS2652  Oct 20, 2019

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