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.
The other equation of the given system of the equation is such that when graphed equations, will form a system with infinitely many solutions are 2x+y=3.
A system of equations to have no real solution, the lines of the equations must be parallel to each other.
1. Dependent Consistent System
A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.
Given to us
6x+3y=9
We know that for the system of lines to give infinite solutions the line must coincide with each other, therefore, the equations must be in ratio to each other.
We can see the given equation that when the equation is divided by 3 from both sides we will get the other equation as 3 is the only common factor on both sides.
[tex]\dfrac{6x+3y}{3}=\dfrac{9 }{3}\\\\2x+y=3[/tex]
Hence, the other equation of the given system of the equation is such that when graphed equations, will form a system with infinitely many solutions are 2x+y=3.
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