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?
- First, determine the values of a.
Find the value of a in both equations.
- Next, determine the value of b.
Find the value of b in both equations
- Next, determine the value of c.
Find the value of c in both equations.
- Finally, calculate x and y.
Using the formulas for linear combination above, calculate x and y.
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.
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.
A slope is the measure of vertical increase over the rise in the horizontal increase of a line.