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Simultaneous Equations

4a - 5b = 7

4a + 5b = 17

Add the two , this will eliminate 'b'

8a = 24

Divide both sides by '8'

a = 3

When a= 3 , substitute into eityher equation for 'b'.

4(3) + 5b = 17

12 + 5b = 17

5b = 17 - 12 = 5

5b = Divide both sides by '5'.

Hence 'b = 1'.

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lenpollock

Lvl 15
1y ago
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Tharindu Senevirathn...

Lvl 3
1y ago

The order pair for the given equations is (4a, 5b). The first element in the pair, 4a, represents the coefficient of the variable a in the equations. The second element in the pair, 5b, represents the coefficient of the variable b in the equations.

You can use the given equations to solve for the values of a and b. For example, to solve for a, you can subtract the second equation from the first equation to get:

4a - 5b - (4a + 5b) = 7 - 17

This simplifies to:

-10b = -10

Therefore, b = 1.

To find the value of a, you can substitute this value back into one of the original equations. For example, substituting b = 1 into the second equation gives:

4a + 5(1) = 17

This simplifies to:

4a + 5 = 17

Therefore, a = 3.

So the solution to the given system of equations is (a,b) = (3,1).

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Mics Sampang

Lvl 3
1y ago

It looks like you have two equations:

4a - 5b = 7

4a + 5b = 17

To find the order pair (a,b) that satisfies both of these equations, you can use the technique of substitution. First, solve one of the equations for one of the variables, such as solving the first equation for a:

a = (7 + 5b)/4

Then substitute this expression for a in the second equation:

4((7 + 5b)/4) + 5b = 17

This simplifies to:

7 + 5b + 5b = 17

Which simplifies to:

12b = 10

Dividing both sides by 12 gives:

b = 10/12

b = 5/6

Substituting this value for b back into the first equation gives:

a = (7 + 5(5/6))/4

a = (7 + 25/6)/4

a = (7 + 25/6)/4

a = (49/6)/4

a = 8/6

a = 4/3

So the order pair that satisfies both equations is (4/3, 5/6).

𝙝𝙩𝙩𝙥𝙨://𝙬𝙬𝙬.𝙙𝙞𝙜𝙞𝙨𝙩𝙤𝙧𝙚24.𝙘𝙤𝙢/𝙧𝙚𝙙𝙞𝙧/372576/𝙨𝙘𝙞𝙢1231/

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Aleigh Kempf

Lvl 5
1y ago

Multiply each equation by the value that makes the coefficients of

a

opposite.

(

1

)

(

4

a

5

b

)

=

(

1

)

(

7

)

4

a

5

b

=

17

Simplify.

Tap for more steps...

4

a

5

b

=

7

4

a

5

b

=

17

Add the two equations together to eliminate

a

from the system.

4

a

5

b

=

7

4

a

5

b

=

1

7

1

0

b

=

1

0

Divide each term in

10

b

=

10

by

10

and simplify.

Tap for more steps...

b

=

1

Substitute the value found for

b

into one of the original equations, then solve for

a

.

Tap for more steps...

a

=

3

This is the final solution to the independent system of equations.

b

=

1

a

=

3

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chinthaginjala venka...

Lvl 5
1y ago
  • 4a-5b=7
  • 4a+5b=17

add two equations

8a=24

a=3

substitute a=3 in second equation

5b=17-4(3)

5b=5

b=1

solution (3,1)

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Do Kim

Lvl 1
1y ago
4a-5b=7

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Wiki User

12y ago

(1) 4a-5b=7

(2) 4a+5b=17

(1)-(2) gives 4a-5b-(4a+5b)=7-17 then -10b=-10 so b=1

from (2) one gets 4a=17-5b=17-5x1=12 so a=3

(3,1) is the solution

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Q: What is the order pair for 4a - 5b equals 7 and 4a plus 5b equals 17?
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