Question

HELP!! Create a system of equations with the solution (-4, 1)

Answer 1

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Answer:

  x -y = -5

  3x +y = -11

Step-by-step explanation:

We assume you want two linear equations. Since you know a point on each line, the only thing you need to choose is the slope of the two lines through that point. We can make the slopes be +1 and -3, for example. Then the point-slope equations are ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

 y -1 = +1(x +4)

  y -1 = -3(x +4)

We can use these equations "as is", or put them in whatever form you like. I personally prefer "standard form:" ax+by=c.

First equation:

  y -1 = x +4 . . . . . . eliminate parentheses

  -5 = x -y . . . . . . . keep positive x term, put x and y together, separate from the constant

  x - y = -5 . . . . . . standard form

Second equation:

  y -1 = -3x -12 . . . . eliminate parentheses

  3x +y = -11 . . . . . . add 3x+1 to both sides

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A system of equations with solution (-4, 1) is ...

• x - y = -5
• 3x + y = -11