Math Problem Statement
Solve the system of equations: x - z = 0, 2x - w = 0, y - w = 0.
Solution
The system of equations presented in the image is:
1. \, & x - z = 0 \\ 2. \, & 2x - w = 0 \\ 3. \, & y - w = 0 \end{aligned}$$ ### Step-by-Step Solution: 1. From equation $$x - z = 0$$, we can express $$z$$ in terms of $$x$$: $$z = x$$ 2. From equation $$2x - w = 0$$, we can express $$w$$ in terms of $$x$$: $$w = 2x$$ 3. From equation $$y - w = 0$$, we can express $$y$$ in terms of $$w$$: $$y = w$$ Substituting $$w = 2x$$ from the previous step: $$y = 2x$$ ### Final Values in Terms of $$x$$: - $$z = x$$ - $$w = 2x$$ - $$y = 2x$$ This system gives the relationships between the variables in terms of $$x$$. Do you want more details or have any questions? --- Here are 5 follow-up questions: 1. What would the system look like if another equation involving $$x, y, z, w$$ is added? 2. How do these solutions change if $$x = 0$$? 3. Can you create a matrix to represent this system of equations? 4. What happens if the second equation is modified to $$2x + w = 0$$? 5. What would a graphical interpretation of this system look like? **Tip**: When solving a system of equations, start by simplifying and substituting step-by-step to avoid mistakes.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Substitution
Formulas
x = z
w = 2x
y = w = 2x
Theorems
System of linear equations solution through substitution
Suitable Grade Level
Grades 9-12