**Definition of System of Equations**

- A System of Equations is a set of two or more equations with the same variables graphed on the same coordinate plane.

**More about System of Equations**

- A linear system of equations involves only linear equations, and similarly, a quadratic system of equations involves only quadratic equations.
- There are various methods such as substitution method, elimination method, Gaussian elimination method, graph-and-check method, etc. by which a system of linear equations can be solved.

**Example of System of Equations**

- The graph given below represents the system of equations,
*x*+*y*= 4 and*x*-*y*= - 2.

- The point of intersection gives the solution for the system of equations.

**Solved Example on System of Equations**

Use graph-and-check method to solve the linear system.

4y=x- 12

y+x= 2

Choices:

A. (2, 4)

B. (4, - 2)

C. (2, - 3)

D. No solution

Correct Answer: B

Solution:

Step 1:4y=x– 12 [Equation 1.]

Step 2:y= 1/4x– 3 [Rewrite in slope intercept form.]

Step 3:y+x= 2 [Equation 2.]

Step 4:y= -x+ 2 [Rewrite in slope intercept form.]

Step 5:Graph the two equations using the slope andy-intercept.

Step 6:It appears that the two lines intersect at the point (4, - 2).

Step 7:Check the solution algebraically:

- 2 = 1/4(4) – 3 [Substitute the values iny= 1/4x- 3.]

Step 8:- 2 = - 2 [Simplify.]

Step 9:- 2 = - 4 + 2 [Substitute the values iny= -x+ 2.]

Step 10:- 2 = - 2 [Simplify.]

Step 11:So, (4, - 2) is the solution of the linear system.

**Related Terms for System of Equations**

- Coordinate plane
- Equations
- System of Inequalities
- Variables