Question

Given 3a - 7b = 29 and 4a + 5b = 67, find the value of (182a - 52b)/97.

Answer 1

To find the value of (182a - 52b)/97, solve for a and b using the system of linear equations provided. Apply elimination method or substitution to determine the values of a and b, then substitute these values into the given expression and simplify to get the result.

Step-by-step explanation:

To find the value of (182a - 52b)/97, we first need to solve the system of equations for a and b. We have:

• 3a - 7b = 29
• 4a + 5b = 67

Now, we need to use a method such as substitution or elimination to solve for a and b. For this example, let's use the elimination method.

Multiply the first equation by 4 and the second by 3 to get:

• 12a - 28b = 116
• 12a + 15b = 201

Subtracting the first new equation from the second gives us:

• 43b = 85

Dividing both sides by 43 gives us b:

b = 85 / 43

To find a, substitute b back into one of the original equations:

• 3a - 7(85/43) = 29

Now, solve for a and substitute the values of a and b into the expression (182a - 52b)/97.