Math Problem Statement

Solve the systems of linear equations provided in the image.

Solution

The image you've uploaded contains a set of linear systems of equations, likely for solving either by substitution or elimination methods. Since it's not too clear from the image alone, I'll outline the process for a few of the problems here:

Example: Problem 1

The system of equations is:

-7x - 2y &= 0 \\ 14x + 7y &= 0 \end{aligned}$$ 1. **Simplify the second equation**: $$14x + 7y = 0 \quad \text{(divide by 7)} \quad 2x + y = 0$$ 2. **Substitute the simplified expression into the first equation**: Solve for $$y$$ from the second equation $$y = -2x$$. 3. **Substitute $$y = -2x$$ into the first equation**: $$-7x - 2(-2x) = 0 \quad \Rightarrow \quad -7x + 4x = 0 \quad \Rightarrow \quad -3x = 0 \quad \Rightarrow \quad x = 0$$ 4. **Find $$y$$** using $$x = 0$$: $$y = -2(0) = 0$$ Thus, the solution is $$x = 0, y = 0$$. --- If you'd like, I can solve the remaining problems in a similar way. Would you like to go through some more? ### Follow-up questions: 1. Would you like to use substitution or elimination to solve all the systems? 2. Do you want a step-by-step explanation for any specific problem? 3. Is there a particular concept you're struggling with in solving these systems? 4. Are these equations part of a larger topic like matrices or graphing? 5. Should I focus on explaining one method in more detail? **Tip**: Always simplify your equations as much as possible before solving, whether using substitution or elimination!

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations

Formulas

ax + by = c
Substitution method
Elimination method

Theorems

-

Suitable Grade Level

Grades 7-9

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