Question

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Answer 1

a = 15

b = - 14

Explanation:

Solve the equation for a

a = 29 + b

Substitute the given value of a into the equation
`(a)/(5)-(b)/(2)=10`

`(29+b)/(5)- (b)/(2) =10`

Solve the equation for b

b = - 14

Substitute the given value of b into the equation a = 29 + b

a = 29 + (- 14)

Solve the equation for a

a = 15

The possible solution of the system is the ordered pair (a, b)

(a, b) = (15, -14)

Check if the given ordered pair is the solution of the system of equations

`(15)/(5) - (-14)/(2) = 10`

`15-(-14) = 29`

Simplify the equalities

10 = 10

29 = 29

Since all of the equalities are true, the ordered pair is the solution of the system

(a, b) = (15, -14)

Answer 2

a = 15

b = -10

Explanation:

Here, we want to solve the system of linear equations

Firstly, let us multiply the first equation through by 10

2a - 5b = 100 ••••(i)

from the second equation;

a = 29 + b

Substitute this into i

2(29 + b) - 5b = 100

58 + 2b -5b = 100

-3b = 100-58

3b = 42

-b = 42/3

-b = 14

recall;

a - b = 29

a - (-14) = 29

a + 14 = 29

a = 29-14 = 15