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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.

Radni primjer · 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}

Korak po korak

  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.

Otkrij odgovor
x = 2,\; y = 1

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Simboli koji se koriste ovdje

Dodirnite bilo koji simbol za punu definiciju, sliku, i što znači svako slovo u njoj.

Kako: Systems of equations

  1. The system has 2 equations in 2 unknowns (x, y).
  2. From the first equation, express x in terms of y.
  3. Substitute that into the second equation, leaving one equation in y.
  4. Solve for y.
  5. Back-substitute to get x.

Pitanja koja ljudi postavljaju

What does it mean to solve an equation?

To find every value of the unknown that makes both sides equal. Each step is an operation applied to both sides that keeps the solution set the same, until the unknown stands alone.

Why do I sometimes get two answers?

A quadratic can cross the axis twice, so it can have two solutions. A degree-n polynomial has up to n. The graph shows where each one comes from.

How do I know whether to factor or use the quadratic formula?

Try factoring for a few seconds: look for two numbers that multiply to a·c and add to b. If nothing obvious appears, the discriminant b² − 4ac tells you how many real roots there are, and the formula finds them without guessing.

Više u Algebra

Linear equationsQuadratic equationsInequalitiesFactoringExpandingSimplifying expressionsFunctions and graphsExponential and logarithmic equationsPolynomial equationsAbsolute value