Respuesta :
Answer:
y = – 3x + 4 and 3y = – 9x + 12, y = –3x + 4 and y = –6x + 8
Step-by-step explanation:
Consider all Options as to solve this problem;
Option A; Here we are given equations y = – 3x + 4 and y = – 3x – 4. A system of equations can only have infinitely many solutions if the two equations are one in the same, such that their graphical representation overlap one another. Now the difference between the two equations is that the second has a y - intercept of - 4, rather 4 such that they are not one in the same equation.
Option B; We are given the following equations; y = – 3x + 4 and 3y = – 9x + 12. Convert the second equation to point - slope form, so that they can easily be compared, by dividing the second equation by 3: 3y = –9x + 12 ⇒ y = - 3x + 4. y = - 3x + 4, and y = - 3x + 4 are one in the same equation, thus this system of equations has infinitely many solutions.
Option C; The equations y = –3x + 4 and y = - 1/3x + 4 are most certainly not the same provided the second equation has a slope of - 1 /3 comparative to that of the first equation's slope, - 3.
Option D; y = –3x + 4 and y = –6x + 8, are one in the same, as if yoy multiply the first equation by 2 you receive the second; y = –6x + 8
Solution( s ); y = – 3x + 4 and 3y = – 9x + 12, y = –3x + 4 and y = –6x + 8
The system of equations y = –3x + 4 and 3y = –9x + 12y has infinitely many solutions.
We need to find the system of equations below has infinitely many solutions.
What is the condition for the system of lines that has infinitely many solutions?
The condition for the system of lines that has infinitely many solutions is [tex]\frac{a_{1} }{a_{2}} =\frac{b_{1} }{b_{2}}=\frac{c_{1} }{c_{2}}[/tex].
Now, y +3x - 4=0 and 3y+9x - 12=0
3/9=1/3=-4/-12=1/3
Therefore, the system of equations y = –3x + 4 and 3y = –9x + 12y has infinitely many solutions.
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