Question

When solving complex systems (2 systems to find what 1 var is), what method is commonly used?

A) Substitution method
B) Factoring method
C) Division method
D) Addition method

Answer 1

The commonly used method to solve complex systems of equations is the Substitution method. This method involves solving one equation for one variable and substituting it into the other equation to find the value of the other variable.

Step-by-step explanation:

The method commonly used to solve complex systems of equations is the Substitution method. This method involves solving one equation for one variable and substituting it into the other equation to find the value of the other variable. Here's how it works:

1. Start by solving one equation for one variable. Let's assume we have two equations: Equation 1: 2x + 3y = 12 and Equation 2: 3x - 2y = 4.
2. Choose one equation to solve for one variable. Let's solve Equation 1 for x: 2x = 12 - 3y ⇒ x = 6 - (3/2)y.
3. Substitute the expression for x obtained in step 2 into the other equation. Let's substitute it into Equation 2: 3(6 - (3/2)y) - 2y = 4.
4. Solve the resulting equation for y: 18 - (9/2)y - 2y = 4 ⇒ 18 - 4 - (9/2)y - 2y = 0 ⇒ -19/2y = -14 ⇒ y = 4/19.
5. Substitute the value of y obtained in step 4 into the expression for x obtained in step 2 to find x. Using x = 6 - (3/2)y and y = 4/19, we get: x = 6 - (3/2)(4/19) ⇒ x = 6 - 12/19 ⇒ x = 114/19 - 12/19 ⇒ x = 102/19.
6. Therefore, the solution to the system of equations is x = 102/19 and y = 4/19.