Question

How many solutions have the pair of linear equations 2x+3y-9=0 and
4x + 6y - 18 = 0?​

Answer 1

Given:

2x+3y-9=0

4x+6y-18=0

To Find:

the solutions of the equation

Solution:

Here $\frac{a_{1} }{a_{2} }$ = $\frac{b_{1} }{b_{2} }=\frac{c_{1} }{c_{2} } =\frac{1}{2}$

So, the given pair of equations has infinitely many solutions.

By Elimination Method,

2x+3y-9=0>2x+3y=9 ..(i)

4x+6y-18=0>4x+6y=18 ..(ii)

Multiplying (i) and (ii) by 2 and subtracting them,

Then, y= 0.6

now, putting y =0.6 in(ii)

⇒ 4x+6y-18=0

⇒ 4x+6(0.6)-18=0

⇒ 4x+3.6-18=0

⇒ -10.4=x

Now, we have both the values of x and y so we substitute the values in the equation.

so,(x, y) = (10.4,0.6)

The given pair of the linear equation can be solved by many other methods. This can also be solved using the graphical method, substitution method, and other methods too.

Answer 2

Answer:

infinitely many solutions