Math Problem Statement
tolong jawab dengan benar.
tolong jawab dengan benar.
Solution
The problem involves solving systems of linear equations using the substitution method. The equations in the image are:
(1)
y = x + 2 \\ 3x + y = 14 \end{cases}$$ **(2)** $$\begin{cases} x + 3y = 3 \\ x = -y + 2 \end{cases}$$ ### Solution for System (1): 1. The first equation $$y = x + 2$$ is already solved for $$y$$. 2. Substitute $$y = x + 2$$ into the second equation $$3x + y = 14$$: $$3x + (x + 2) = 14$$ 3. Simplify and solve for $$x$$: $$3x + x + 2 = 14$$ $$4x + 2 = 14$$ $$4x = 12$$ $$x = 3$$ 4. Substitute $$x = 3$$ back into the first equation $$y = x + 2$$ to find $$y$$: $$y = 3 + 2 = 5$$ So, the solution for the first system is $$x = 3$$ and $$y = 5$$. ### Solution for System (2): 1. The second equation $$x = -y + 2$$ is already solved for $$x$$. 2. Substitute $$x = -y + 2$$ into the first equation $$x + 3y = 3$$: $$(-y + 2) + 3y = 3$$ 3. Simplify and solve for $$y$$: $$- y + 2 + 3y = 3$$ $$2y + 2 = 3$$ $$2y = 1$$ $$y = \frac{1}{2}$$ 4. Substitute $$y = \frac{1}{2}$$ back into the equation $$x = -y + 2$$ to find $$x$$: $$x = -\frac{1}{2} + 2 = \frac{3}{2}$$ So, the solution for the second system is $$x = \frac{3}{2}$$ and $$y = \frac{1}{2}$$. ### Summary: - **System 1:** $$x = 3$$, $$y = 5$$ - **System 2:** $$x = \frac{3}{2}$$, $$y = \frac{1}{2}$$ Would you like more details or have any other questions? Here are some related questions: 1. What is the graphical interpretation of these solutions? 2. Can we solve these systems using the elimination method? 3. What happens if the equations in a system are parallel? 4. How do you determine if a system has no solution? 5. How can you verify the solution to a system of linear equations? **Tip:** When solving systems of equations, always double-check by substituting the solution back into the original equations to ensure accuracy.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Systems of Linear Equations
Substitution Method
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12
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