Question

What is the solution of the following system of equations by 3x-2y=12 6x-4y=24

Answer 1

Answer:

Infinitely many solutions.

Step-by-step explanation:

Given

$3x-2y=12\\ 6x-4y=24$

Required;

Find the solution

$3x-2y=12 --(1)\\ 6x-4y=24 -- (2)$

Make x the subject of formula in (1)

$3x-2y=12$

Add 2y to both sides

$3x-2y+2y=12+2y$

$3x=12+2y$

Divide both sides by 3

$\frac{3x}{3}=\frac{12+2y}{3}$

$x=\frac{12+2y}{3}$

Substitute $x=\frac{12+2y}{3}$ in (2)

$6x-4y=24$

$6(\frac{12+2y}{3})-4y=24$

$2(12+2y)-4y=24$

Open Bracket

$24+4y-4y=24$

$24+4y-4y=24$

Collect Like Terms

$4y-4y=24-24$

$0 = 0$

Based on the result above, the two equations have infinitely many solutions.