Cara mudah sistem persamaan linear dua variabel menggunakan metode eliminasi, subtitusi dan campuran

Summary

The video explains how to solve a system of two linear equations in two variables using elimination, substitution, and a combination of both methods. The example is:

[ \begin{aligned} 3x + 2y &= 5 \ 4x + 3y &= 6 \end{aligned} ]

Although some subtitles are garbled, the repeated calculations indicate that the second equation is (4x + 3y = 6). All three methods give the solution (x = 3), (y = -2).

1. Elimination method

The goal is to make one variable’s coefficients match, then add or subtract the equations to cancel that variable.

Eliminate (y):

• Multiply the first equation by 3: (9x + 6y = 15).
• Multiply the second equation by 2: (8x + 6y = 12).
• Subtract the second equation from the first: (x = 3).

Eliminate (x):

• Multiply the first equation by 4: (12x + 8y = 20).
• Multiply the second equation by 3: (12x + 9y = 18).
• Subtract the first equation from the second: (y = -2).

The presenter’s sign rule is: after matching coefficients, subtract when the terms to be eliminated have the same sign; add when they have opposite signs.

2. Substitution method

The goal is to rearrange one equation to express one variable in terms of the other, then substitute that expression into the second equation.

Rearrange (3x + 2y = 5) to make (y) the subject:

[ y = \frac{5 - 3x}{2} ]

Substitute this into (4x + 3y = 6):

[ 4x + 3\left(\frac{5 - 3x}{2}\right) = 6 ]

Multiply through by 2 and solve:

[ 8x + 15 - 9x = 12 \quad\Rightarrow\quad x = 3 ]

Substitute (x = 3) back into (y = \frac{5 - 3x}{2}):

[ y = \frac{5 - 9}{2} = -2 ]

3. Mixed method

The mixed method uses elimination first, then substitution.

• Eliminate (y), as in the first method, to find (x = 3).
• Substitute (x = 3) into the second equation:

[ 4(3) + 3y = 6 ]

• Solve to get (y = -2).

The video’s main lesson is that the methods use different steps but produce the same solution. You can choose either variable to eliminate or either equation to use for substitution.

Speakers and sources

• One presenter speaks for the Matematika Hebat channel. No other speakers or sources are featured.