Solve the following system of equations: 3x - 2y = 6, 6x - 4y = 12.

Solution:

Given, the system of equations

3x - 2y = 6 --- (1)

6x - 4y = 12 --- (2)

We have to solve the system of equations.

Dividing (2) by 2,

3x - 2y = 6 which is same as equation (1)

Thus, the system will have many infinite solutions.

For a system of equation having infinite solution following condition holds:

\(\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}\)

Here, a₁ = 3, b₁ = -2, c₁ = 6

a₂ = 6, b₂ = -4, c₂ = 12

Now, \(\\\frac{3}{6}=\frac{-2}{-4}=\frac{6}{12}\\\frac{1}{2}=\frac{1}{2}=\frac{1}{2}\)

Therefore, \(\\\frac{3}{6}=\frac{-2}{-4}=\frac{6}{12}=\frac{1}{2}\)

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Solve the following system of equations: 3x - 2y = 6, 6x - 4y = 12.

Summary:

The system of equations: 3x - 2y = 6, 6x - 4y = 12 will have many infinite solutions.