Solve the following system of equations for a and for b

:
System of Equations:

Value of a

Value of b
9a+3b=30

8a+4b=28

1 answer

To solve the system of equations:

  1. 9a+3b=30 (Equation 1)
  2. 8a+4b=28 (Equation 2)

We can simplify both equations.

Starting with Equation 1, we can divide every term by 3:

3a+b=10(Equation 3)

Now, let's simplify Equation 2 by dividing every term by 4:

2a+b=7(Equation 4)

Now we have the simplified system:

  1. 3a+b=10 (Equation 3)
  2. 2a+b=7 (Equation 4)

Next, we can eliminate b by subtracting Equation 4 from Equation 3:

(3a+b)(2a+b)=107

This simplifies to:

3a2a+bb=3

So, we have:

a=3

Now, we can substitute this value of a back into either Equation 3 or Equation 4 to find b. Using Equation 4:

2(3)+b=7

This becomes:

6+b=7

Subtracting 6 from both sides gives:

b=1

Thus, the solution to the system of equations is:

a=3,b=1