Question

Check given systems of equations to see if it has a unique solution, infinitely many solutions or no solution. Solve them graphically.
x + 2y = 6
2x + 4y = 12

Answer 1

Dear student,

Answer: Both lines are coincident lines, thus have infinitely many solutions

Solution:

To find the equation of line ,you should find three points to draw the straight line, for that just put any value of x, and calculate the value of y, buy this way find three points, of each equation.

$x + 2y = 6 \\ \\ put \: x = 0 \\ y = 3 \\ x = 2 \\ y = 2 \\ \\ x = 4 \\ y = 1$
so,points are (0,3), (2,2) and (4,1)

for second equation

$2x + 4y = 12 \\ \\ put \: x \: = 0 \\ y = 3 \\ \\ put \: x = 2 \\ y = 2 \\ \\ put \: x =4 \\ \\ y = 1$
Again points are (0,3) ,(2,2) and (4,1)

since both equation have all three point same that means both are coincident lines,
Thus, the pair of linear equations has infinitely many solution.

Graph: for your easy understanding of graph I am showing both lines with different colour and with different pattern.

hope the solution helps you

Answer 2

Answer:

Step-by-step explanation: