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Systems of equationsAlgebraHigh schoolabout 1:05

Solve the system x^2 + y^2 = 25, x - y = 1: animated lesson

A narrated, step-by-step systems of equations video lesson with captions. Final answer: (x, y) = (-3, -4) or (x, y) = (4, 3).

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 (0.4 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Solving an equation
    x^2 + y^2 = 25; x - y = 1
  2. 2. Step by step
    1. {x2+y2=25x−y=1\begin{cases} {x}^{2}+{y}^{2} = 25 \\ x- y = 1 \end{cases}
      Read the system
    2. Solve equation 2 for x
    3. Substitute into equation 1
    4. Back-substitute to find x
  3. 3. The answer
    (x, y) = (-3, -4) or (x, y) = (4, 3)\text{(x, y) = (-3, -4) or (x, y) = (4, 3)}

    (x, y) = (-3, -4) or (x, y) = (4, 3)

  4. 4. Check
    • (-3, -4) satisfies both equations ✓
    • (4, 3) satisfies both equations ✓

Transcript

The problem. Here is the problem: x squared plus y squared equals 25; x minus y equals 1. A nonlinear system of 2 equations in x and y.

Step by step. Read the system. Solve equation 2 for x. Equation 2 is linear in x, so x can be written in terms of y. Substitute into equation 1. This leaves one equation in y; its real roots are y equals negative 4, y equals 3. Back-substitute to find x. (x, y) equals (negative 3, negative 4); (x, y) equals (4, 3).

The answer. So the answer is (x, y) equals (negative 3, negative 4) or (x, y) equals (4, 3). Solving one equation for a variable and substituting turns the system into a single equation in one unknown; each root gives one solution pair.

Check. (negative 3, negative 4) satisfies both equations, which checks out. (4, 3) satisfies both equations, 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^2 + y^2 = 25, x - y = 1: Animated Lesson