Question

Solve the given system By graphing if there is no solution or an infinite number of solutions so state you set notation to express solution sets. { 2x-4y=8, 3X+4y=12 }
WHAT ARE THE POINTS ON A GRAPH? Helppp

Answer 1

Answer:

  (x, y) ∈ { (4, 0) }

Step-by-step explanation:

When the equations are in standard form (or close to it), it is often convenient to graph them using their x- and y-intercepts. The x-intercept is found by setting y=0 and solving for x. The y-intercept is found by setting x=0 and solving for y.

2x -4y = 8

  x-intercept = 8/2 = 4

  y-intercept = 8/-4 = -2

3x +4y = 12

  x-intercept = 12/3 = 4

  y-intercept = 12/4 = 3

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The two x-intercepts are the same, so that is the solution to the system of equations: (x, y) = (4, 0). There are various ways to write this in set notation. Simply listing the set of solutions is one of them: { (4, 0) }.

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Additional comment

Standard form is ax+by=c, where 'a' is positive and a, b, c are mutually prime integers (have no common factors). In the first equation, all of the coefficients are even, so 2 is a common factor. In standard form, that equation would be ...

  x -2y = 4