Question

If the ordered pairs (3a+4b,5a-3b)and (29,0) then find a and b.​

Answer 1

Answer:

To solve a system of linear equations that are both in standard form, the most efficient method to use would be the "elimination method".

Step-by-step explanation:

To carry out elimination, you need to alter one (or both) of the equations so as to have one of the variables (and their coefficient) match the same one in another equation.

In your example, you have:

1) 5a+3b=17

2) 4a−5b=21

Say I want to solve for b, this means I need to eliminate a. To do this, I need to multiply eq. 1 by 4 and eq. 2 by 5 like so:

1) 4[5a+3b=17]

2) 5[4a−5b=21]

This results in:

1) 20a+12b=68

2) 20a−25b=105

Now, if the variable you are trying to eliminate has the same sign in both equations, you subtract the equations. If the signs are opposite, you add them. To remember this, think OASS (opposite, add, same, subtract). In this case, the signs are the same so you want to subtract the equations, resulting in:

(20a−20a)−(12b−25b)=(68−105)

37b=−37

b=−1

Now that you have b, you can substitute that back into one of the original equations to solve for a. I'll sub it into eq. 1:

5a+3(−1)=17

Solving for a:

5a=20

a=4

Therefore, your solution set (or point of intersection) is (4, -1).

Hopefully, this was all clear and I hope you found it helpful! :)

Answer 2

Appropriate Question :-

If the ordered pairs (3a+4b,5a-3b)and (29,0) are equal then find a and b.

Solution :-

Given that

(3a+4b,5a-3b)and (29,0) are equal.

We know that

(x,y) = (a,b) => x = a and y = b

Therefore, 3a+4b = 29 -----------(1)

and 5a-3b = 0 ----------------------(2)

=> 5a = 0+3b

=> 5a = 3b

=> a = 3b/5 --------------------------(3)

On substituting the value of a in (1) then

=> 3(3b/5)+4b = 29

=> (9b/5)+4b = 29

=> (9b+20b)/5 = 29

=> 29b/5 = 29

=> 29b = 29×5

=> b = 29×5/29

=> b = 5

Therefore, The value of b = 5

On substituting the value of b in (3) then

a = 3(5)/5

=> a = 15/5

=> a = 3

Therefore, The value of a = 3

Answer :-

The value of a = 3

The value of b = 5

Check :-

If a = 3 and b = 5 then the value of 3a+4b

= 3(3)+4(5)

= 9+20

= 29

Therefore, 3a+4b = 29

If a = 3 and b = 5 then the value of 5a-3b

= 5(3)-3(5)

= 15-15

= 0

Therefore, 5a-3b = 0

Therefore, (3a+4b,5a-3b) = (29,0)

Verified the given relations in the given problem.

Used formulae:-

→ (x,y) = (a,b) => x = a and y = b

Used Method :-

→ Substitution Method