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:
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 [tex]\frac{a}{5}-\frac{b}{2}=10[/tex]
[tex]\frac{29+b}{5}- \frac{b}{2} =10[/tex]
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
[tex]\frac{15}{5} - \frac{-14}{2} = 10[/tex]
[tex]15-(-14) = 29[/tex]
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)
