Question

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Answer 1

Answer:

a = 15

b = -10

Step-by-step 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

Answer 2

Answer:

a = 15

b = - 14

Step-by-step explanation:

Solve the equation for a

a = 29 + b

Substitute the given value of a into the equation  $\frac{a}{5}-\frac{b}{2}=10$

$\frac{29+b}{5}- \frac{b}{2} =10$

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

$\frac{15}{5} - \frac{-14}{2} = 10$

$15-(-14) = 29$

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)