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Systems of equationsAlgebraHigh schoolabout 1:13

Solve the system 4x - 7y = 17 and -2x - 8y = 26: animated lesson

A narrated, step-by-step systems of equations video lesson with captions. Final answer: x = -1, y = -3.

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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. The problem
Solving an equation
$\begin{cases} 4x-7y = 17 \\ -2x-8y = 26 \end{cases}$
2. Steps, part 1
1. $\begin{cases} 4x - 7y = 17 \\ -2x - 8y = 26 \end{cases}$
  Write every equation in standard form
2. $\begin{bmatrix}4 & -7 & 17 \\ -2 & -8 & 26\end{bmatrix}$
  Build the augmented matrix [A | b]
3. Gauss–Jordan elimination
4. $R_{1} \to \tfrac{1}{4} R_{1}:\ \begin{bmatrix}1 & -\frac{7}{4} & \frac{17}{4} \\ -2 & -8 & 26\end{bmatrix}$
  Divide R1 by 4
3. Steps, part 2
1. $R_{2} \to R_{2} + 2R_{1}:\ \begin{bmatrix}1 & -\frac{7}{4} & \frac{17}{4} \\ 0 & -\frac{23}{2} & \frac{69}{2}\end{bmatrix}$
  Clear column 1 using the pivot in R1
2. $R_{2} \to \tfrac{1}{-\frac{23}{2}} R_{2}:\ \begin{bmatrix}1 & -\frac{7}{4} & \frac{17}{4} \\ 0 & 1 & -3\end{bmatrix}$
  Divide R2 by -23/2
3. $R_{1} \to R_{1} + \frac{7}{4} R_{2}:\ \begin{bmatrix}1 & 0 & -1 \\ 0 & 1 & -3\end{bmatrix}$
  Clear column 2 using the pivot in R2
4. $\begin{bmatrix}1 & 0 & -1 \\ 0 & 1 & -3\end{bmatrix}$
  Reduced row-echelon form
4. Steps, part 3
1. $x = -1,\ y = -3$
  Read off the unique solution
5. The answer
$x = -1,\ y = -3$
4x - 7y = 17; -2x - 8y = 26 ⇒ x = -1, y = -3
6. Check
- Equation 1: 4x - 7y = 17 ✓
- Equation 2: -2x - 8y = 26 ✓

Transcript

The problem. Here is the problem: 4x minus 7y equals 17; negative 2x minus 8y equals 26. 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 4.

Steps, part 2. Clear column 1 using the pivot in R1. Divide R2 by negative 23 over 2. 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 negative 1, y equals negative 3. The system has exactly one solution; substituting it back satisfies every equation.

Check. Equation 1: 4x minus 7y equals 17, which checks out. Equation 2: negative 2x minus 8y equals 26, which checks out.

About systems of equations

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

Solve the system 4x - 7y = 17 and -2x - 8y = 26 (Lesson)