Enter the coefficients of x and y of two separate equations into the calculator. The linear combination calculator will solve for both x and y.

Linear Combination Formula

The following formula can be used to calculate the x and y values of two equations using the linear combination.

ax + by = c

dx + ey = f

x =( c – by )/ a = (f -ey)/d

y = (f-dx)/e = (c-ax)/b

  • Where x and y are the coordinate points
  • a and b are coefficients in one equation
  • d and e are coefficients in the other equation
  • f and c are constants

To calculate the linear combination, evaluate the coefficients and constants in each equation, then solve for the x and y values separately using the formulas above.

Linear Combination Definition

A linear combination is a relationship between two equations in the formula ax + by = c. The two equations allow you to solve for missing values of x and y if a, b, and c, are known.

Linear Combination Example

How to calculate a linear combination?

  1. First, determine the values of a.

    Find the value of a in both equations.

  2. Next, determine the value of b.

    Find the value of b in both equations

  3. Next, determine the value of c.

    Find the value of c in both equations.

  4. Finally, calculate x and y.

    Using the formulas for linear combination above, calculate x and y.


What is linear combination?

A linear combination is a mathematical process that involves two related equations. These equations are both in the form ax + by = c. Knowing the values of a, b, and c from both equations one can calculate the missing values of x and y that would solve those equations.

What are x and y coefficients?

The x and y coefficients are values that represent the change in true x and y values with respect to the equation or line the equation represents.

What is a slope?

A slope is the measure of vertical increase over the rise in the horizontal increase of a line.