Math Problem Statement
giải bài 1c như thế nào?
Solution
To solve the system of linear equations given in Bài 1c, we can use either the substitution method or the elimination method. The system is:
0.5x + 0.8y = 0.4 \\ 0.4x - 0.9y = 1.7 \end{cases}$$ Let's use the elimination method to solve this system. First, let's multiply the first equation by 4 and the second equation by 5 to eliminate the decimals: $$\begin{cases} (0.5x + 0.8y = 0.4) \times 4 \implies 2x + 3.2y = 1.6 \\ (0.4x - 0.9y = 1.7) \times 5 \implies 2x - 4.5y = 8.5 \end{cases}$$ Now we have: $$\begin{cases} 2x + 3.2y = 1.6 \\ 2x - 4.5y = 8.5 \end{cases}$$ Next, let's subtract the second equation from the first equation to eliminate $$2x$$: $$(2x + 3.2y) - (2x - 4.5y) = 1.6 - 8.5$$ Simplifying this, we get: $$7.7y = -6.9$$ Solving for $$y$$: $$y = \frac{-6.9}{7.7} \approx -0.896$$ Now that we have $$y$$, we can substitute it back into one of the original equations to solve for $$x$$. Let's use the first equation: $$0.5x + 0.8(-0.896) = 0.4$$ Simplifying: $$0.5x - 0.7168 = 0.4$$ Solving for $$x$$: $$0.5x = 0.4 + 0.7168$$ $$0.5x = 1.1168$$ $$x = \frac{1.1168}{0.5} = 2.2336$$ So, the solution to the system of equations is: $$x \approx 2.234, \quad y \approx -0.896$$ Would you like more details or have any questions? Here are some additional problems you might want to explore: 1. Solve the system of equations in Bài 1a. 2. Solve the system of equations in Bài 1b. 3. Solve the system of equations in Bài 1d. 4. Find the value of $$m$$ so that the system in Bài 4 has a unique solution. 5. Determine the values of $$m$$ so that the system in Bài 5 has a unique solution. Tip: When solving systems of equations, always check your solution by substituting back into the original equations to verify your answer.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Systems of Linear Equations
Elimination Method
Formulas
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Theorems
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Suitable Grade Level
High School