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:
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.
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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
