maths.free › Algebra › Systems of equations

Systems of equations

Substitution and elimination, and what the intersecting lines mean.

Two equations in two unknowns are two lines; the solution is where they cross. Substitution solves one equation for a variable and pushes it into the other. For bigger systems the same idea becomes row reduction on the augmented matrix.

ಕಾರ್ಯಗತಗೊಂಡ ಮಾದರಿ: x + y = 3, x - y = 1

Algebra · Systems-Of-Equations

Solve the system x + y = 3

\begin{cases}x + y = 3 \\ x - y = 1\end{cases}

ಅಡಿಯಿಡು (step)

  1. \begin{cases}x + y = 3 \\ x - y = 1\end{cases}

    The system has 2 equations in 2 unknowns (x, y).

  2. x = 3 - y

    From the first equation, express x in terms of y.

  3. 2 - 2 y = 0

    Substitute that into the second equation, leaving one equation in y.

  4. y = 1

    Solve for y.

  5. x = 3 - y = 2

    Back-substitute to get x.

ಉತ್ತರವನ್ನು ತಿಳಿಸಿ
x = 2,\; y = 1

ನಿಮ್ಮದೇ ಆದದ್ದನ್ನು ಪ್ರಯತ್ನಿಸಿ

ಇನ್ನಷ್ಟು Algebra

Linear equationsQuadratic equationsInequalitiesFactoringExpandingSimplifying expressionsFunctions and graphsExponential and logarithmic equationsPolynomial equationsAbsolute value