What is the best way to solve these eqations with 4 unknowns?

Question

There are 4 equations, and four unknowns to solve for:

$2A+2B=34$

$A+B+C+D=22$

$A+2B+D=31$

$B+3C=17$

Find the value of A, B, C, D.

How do I go about solving this?

Answer 1

Hints:

• Method 1: Set up and solve the system using Gaussian Elimination.
• Method 2: Use substitution and eliminate variables, for example, from the fourth equation we have $B = 17-3C$, substitute into other equations and eliminate and continue this process.
• Method 3: From equation 1, we have $A+B = 17$, like Method 2, use it to reduce and solve.

You should get:

$$A = 6, B = 11, C = 2, D = 3$$