system of equations


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 and y-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 in y = 1/4x - 3.]
Step 8: - 2 = - 2 [Simplify.]
Step 9: - 2 = - 4 + 2 [Substitute the values in y = - 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