Solve System of Linear Equations with Three Variables

Math Problem Statement

Nilai a yang memenuhi SPLTV \(3a + 2b - c = -3, 5b - 2c = 2, 5c = 20\) adalah .....

The given system of linear equations (SPLTV) can be written as:

1. \quad 3a + 2b - c &= -3 \\ 2. \quad 5b - 2c &= 2 \\ 3. \quad 5c &= 20 \end{aligned}$$ Let's solve this system step by step. ### Step 1: Solve the third equation for $$c$$ From the third equation: $$5c = 20$$ Divide both sides by 5: $$c = 4$$ ### Step 2: Substitute $$c = 4$$ into the second equation Substitute $$c = 4$$ into the second equation: $$5b - 2(4) = 2$$ $$5b - 8 = 2$$ Add 8 to both sides: $$5b = 10$$ Divide by 5: $$b = 2$$ ### Step 3: Substitute $$b = 2$$ and $$c = 4$$ into the first equation Now substitute $$b = 2$$ and $$c = 4$$ into the first equation: $$3a + 2(2) - 4 = -3$$ Simplify: $$3a + 4 - 4 = -3$$ $$3a = -3$$ Divide by 3: $$a = -1$$ ### Final Answer: The value of $$a$$ that satisfies the system of linear equations is $$a = -1$$. Would you like more details or have any questions? Here are 5 related questions you could explore: 1. How do we solve a system of three linear equations in general? 2. What is the substitution method in solving systems of equations? 3. How do you check if the solution for a system of equations is correct? 4. What is the elimination method, and how does it differ from substitution? 5. Can every system of linear equations be solved, and under what conditions? **Tip:** When solving systems of equations, it's often helpful to start by solving the simplest equation first, like we did with $$5c = 20$$.

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