lumei
Answered

Can someone please help me ASAP? Please show work. It’s due today!


I will give brainliest if it’s correct!

Can someone please help me ASAP Please show work Its due today I will give brainliest if its correct class=


Answer :

Answer:

  • Both equations reduce to x -2y = 8

Step-by-step explanation:

You want to see the work that demonstrates this system of equations has infinitely many solutions:

  • 4x -8y = 32
  • 2x -4y = 16

Standard form

The standard form of an equation for a line is ...

  ax +by = c

where a, b, c are mutually prime and a > 0.

We can put each of these equations in standard form by dividing by the coefficient of x:

Equation 1:

  [tex]\dfrac{4x -8y}{4}=\dfrac{32}{4}\\\\x-2y=8[/tex]

Equation 2:

  [tex]\dfrac{2x -4y}{2}=\dfrac{16}{2}\\\\x-2y=8[/tex]

Infinitely many solutions

The two equations are identical when written in the same form. This means any of the infinitely many solutions to one of them will also be a solution of the other equation.

__

Additional comment

You can settle on this set of equations by looking at the relationships of the coefficients in each set of equations. If the ratio of x to y coefficients is the same, there will be infinitely many solutions if the ratio of constants is the same as the ratio of the x coefficients. If the ratios x/y are different, the system has 1 solution.

Set 1: x/y coefficients = -3/4 and 2/2 . . . . one solution

Set 2: analysis is shown above

Set 3: -9/3 = -1/3, but 27/12 is not the same . . . . no solutions

Set 4: 4.25/7 and 3/2 . . . . one solution

Answer:

2 and 3 have infinitely many solutions.

Step-by-step explanation:

Please find the attached.

Determinant of the coefficients of the unknowns (x and y) is zero, therefore 2 and 3 have infinitely many solutions.

View image olumideolawoyin