Question

Consider the equation 6x+3y=9. Which equation, when graphed with the given equation, will form a system with infinitely many solutions? y+2x=3 y+2x=9 y=2x+3 or y=-2x+9

Answer 1

Answer:

a. y+2x=3

Step-by-step explanation:

Consider the equation 6x+3y=9. Which equation, when graphed with the given equation, will form a system with infinitely many solutions? y+2x=3 y+2x=9 y=2x+3 or y=-2x+9

Two equations with two unknowns do not always have a unique solution.

6x+3y=9

solving simultaneously with equation 1

6x+3y=9

y+2x=3

rearranging the second equation , we have

6x+3y=9..............................1

2x+y=3..................................2

multiplying the second equation by 2

6x+3y=9..............................1

2x+y=3..................................2   x3

6x+3y=9..............................1

6x+3y=9..................................2

introduce a minus sign, we ave

x=0, y=0

to prove that it has infinitely many solutions

the others will converge at a point when solve simultaneous with given algebriac equation.

Answer 2

Lol that confusing wording; but I assume what you mean is what line is equal to 6x + 3y = 9, therefore giving the same solutions.

First of, You would need to convert 6x + 3y = 9 to Slope/Y-Intercept form.

6x + 3y = 9
   6x - 9 = -3y
  /-3  /-3 = /-3
 -2x - 3 = Y

Since the equation above is not equal to any of your responses, it is not C or D. (That is not the case if your given information or teacher made a mistake)

So, Find a line that is proportionate to 6x - 3y = 9 using LCD's

6x + 3y = 9
/3   /3     /3
2x + Y = 3

Since the equation is above is equal to A, the solution is A.