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Systems of equationsAlgebraHigh schoolabout 1:14

Solve the system -x + 6y = -44 and -2x + 7y = -58: animated lesson

A narrated, step-by-step systems of equations video lesson with captions. Final answer: x = 8, y = -6.

Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.5 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Solving an equation
    {−x+6y=−44−2x+7y=−58\begin{cases} - x+6y = -44 \\ -2x+7y = -58 \end{cases}
  2. 2. Steps, part 1
    1. {−x+6y=−44−2x+7y=−58\begin{cases} -x + 6y = -44 \\ -2x + 7y = -58 \end{cases}
      Write every equation in standard form
    2. [−16−44−27−58]\begin{bmatrix}-1 & 6 & -44 \\ -2 & 7 & -58\end{bmatrix}
      Build the augmented matrix [A | b]
    3. Gauss–Jordan elimination
    4. R1→1−1R1: [1−644−27−58]R_{1} \to \tfrac{1}{-1} R_{1}:\ \begin{bmatrix}1 & -6 & 44 \\ -2 & 7 & -58\end{bmatrix}
      Divide R1 by -1
  3. 3. Steps, part 2
    1. R2→R2+2R1: [1−6440−530]R_{2} \to R_{2} + 2R_{1}:\ \begin{bmatrix}1 & -6 & 44 \\ 0 & -5 & 30\end{bmatrix}
      Clear column 1 using the pivot in R1
    2. R2→1−5R2: [1−64401−6]R_{2} \to \tfrac{1}{-5} R_{2}:\ \begin{bmatrix}1 & -6 & 44 \\ 0 & 1 & -6\end{bmatrix}
      Divide R2 by -5
    3. R1→R1+6R2: [10801−6]R_{1} \to R_{1} + 6R_{2}:\ \begin{bmatrix}1 & 0 & 8 \\ 0 & 1 & -6\end{bmatrix}
      Clear column 2 using the pivot in R2
    4. [10801−6]\begin{bmatrix}1 & 0 & 8 \\ 0 & 1 & -6\end{bmatrix}
      Reduced row-echelon form
  4. 4. Steps, part 3
    1. x=8, y=−6x = 8,\ y = -6
      Read off the unique solution
  5. 5. The answer
    x=8, y=−6x = 8,\ y = -6

    -x + 6y = -44; -2x + 7y = -58 ⇒ x = 8, y = -6

  6. 6. Check
    • Equation 1: -x + 6y = -44 ✓
    • Equation 2: -2x + 7y = -58 ✓

Transcript

The problem. Here is the problem: negative x plus 6y equals negative 44; negative 2x plus 7y equals negative 58. 2 linear equations in 2 unknowns (x, y).

Steps, part 1. Write every equation in standard form. Move all variable terms to the left and constants to the right. Build the augmented matrix [A | b]. Columns: x, y | constant. Gauss–Jordan elimination. Use row operations to make each pivot 1 and clear the rest of its column. Divide R1 by negative 1.

Steps, part 2. Clear column 1 using the pivot in R1. Divide R2 by negative 5. Clear column 2 using the pivot in R2. Reduced row-echelon form.

Steps, part 3. Read off the unique solution.

The answer. So the answer is x equals 8, y equals negative 6. The system has exactly one solution; substituting it back satisfies every equation.

Check. Equation 1: negative x plus 6y equals negative 44, which checks out. Equation 2: negative 2x plus 7y equals negative 58, which checks out.

About systems of equations

Solve systems of two or three linear equations by elimination and substitution.

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Solve the system -x + 6y = -44 and -2x + 7y = -58 (Lesson)