To solve the system of linear equations 15a - 4b = 25 and 5a + 2b = 2, we can use the method of elimination or substitution. Using the method of elimination, we multiply the second equation by 3 to eliminate the 'b' term, subtract the second equation from the first equation to eliminate the 'a' term, and solve for the values of a and b. The values that satisfy both equations simultaneously are a = 11/15 and b = -19/7.
Step-by-step explanation:
To solve the system of linear equations:
15a - 4b = 25
5a + 2b = 2
We can use the method of elimination or substitution to find the values of a and b that satisfy both equations simultaneously.
Using the method of elimination:
Multiply the second equation by 3 to eliminate the 'b' term: 15a - 4b = 25 and 5(3a + b) = 3(2)
Distribute the multiplication: 15a - 4b = 25 and 15a + 3b = 6
Subtract the second equation from the first equation to eliminate the 'a' term: (15a - 4b) - (15a + 3b) = 25 - 6
Simplify the equation: -7b = 19
Divide both sides of the equation by -7: b = -19/7
Substitute the value of 'b' back into one of the original equations to solve for 'a': 15a - 4(-19/7) = 25
Simplify and solve for 'a': 15a + 76/7 = 25
Subtract 76/7 from both sides of the equation: 15a = 25 - 76/7
Convert mixed number to an improper fraction: 15a = 175/7 - 76/7
Combine the fractions: 15a = 99/7
Divide both sides of the equation by 15 to solve for 'a': a = (99/7) / 15
Divide the fractions: a = 99/105
Simplify the fraction: a = 11/15
Therefore, the values of a and b that satisfy both equations simultaneously are a = 11/15 and b = -19/7.
The probale question can be:
"Given the system of linear equations:
15a - 4b &= 25
5a + 2b &= 25
Find the values of a and b that satisfy both equations simultaneously."