In mathematics, a system with two unknowns has two mathematical expressions involving two variables, but for which we can not know the value until the resolution of the system itself. In today’s article we will see precisely how to solve it, that is, to discover the value of the two variables that is initially unknown. Lets talk about how to calculate a system with two unknowns.

how to calculate

Step 1

Consider, for example, the system of equations thus formed: the first equation is 3x + 4y = 18, while the second is represented by the expression 2x + 2y = 10. In general, being two equations of the first degree (given that not are entitlement power of unknowns), where the variables are not known exactly two (represented by the letters x and y), you can always conclude that the solution can be identified.

Step 2

To solve this system we will start our analysis from the second equation, 2x + 2y = 10. Taking advantage of the associative property of the sum, this equation could be rewritten as 2 * (x + y) = 10. Then, through a simple step algebraic (division by two of both members of the current equation) we can also say that (x + y) = 10/2 = 5. And also, consequently, x will be equal to 5-y.

Step 3

The information obtained in the previous step is very important! In fact, now we can go back to focus our attention on the first equation of the system, 3x + 4y = 18, substituting instead of the variable x, just 5 – y. In summary, we now know that 3 * (5 – y) + 4y = 18. So 15 – 3y + 4y = 18. Now, moving the first term (number 15) in the second member of the equation, suitably changed sign and adding algebraically multipliers y (+4 -3), we obtain finally own the value of y, which is in fact equal to 3. Since we already knew that x = 5 – y, then we can get the value of x, 5-3 = 2. Since we now have discovered the value of the two unknowns, we can safely say we have arrived at the solution of our system!