https://file.aiquickdraw.com/mathbot/file/17294625344834n61i3xt.jpg

The image shows a set of algebraic equations along with corresponding steps on the right-hand side labeled with actions like "Multiplication prop," "Addition prop," and others.

Let me go through the parts:

### Left Column (Labeled S):
1. \( 3x + 5y = 2 \)
2. \( x + 4y = -4 \)
3. \( -1(3x + 5y) = (2)(-1) \)
4. \( 3(x + 4y) = (-4)(3) \)
5. \( -3x + -5y = -2 \)
6. \( 3x + 12y = -12 \)
7. \( -3x + 12y = -14 \)
8. \( y = -2 \)
9. \( 3x + 5(-2) = 2 \)
10. \( 3x - 10 = 2 \)

### Right Column (Labeled R):
1. Given
2. Given
3. Multiplication prop (property)
4. Multiplication prop
5. Distributive prop
6. Distributive prop
7. Elimination
8. Substitution
9. Division prop
10. Multiplication prop
11. Addition prop
12. Division prop

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It seems this is part of solving a system of linear equations using substitution or elimination. The steps involve manipulating the two equations, applying properties of equality like distribution, multiplication, and substitution, to find the value of \( y \) and \( x \).

If you'd like, I can help verify each step, or go through the solution in more detail.

Would you like further explanation of specific parts?

### Questions:
1. Would you like help solving for \( x \) after \( y = -2 \)?
2. Should we break down the properties (like multiplication and substitution) step by step?
3. Are you familiar with how elimination is used to solve systems of equations?
4. Would you like a more detailed explanation of how substitution was applied?
5. Would you like to check if the system has a unique solution, or if it's consistent?

### Tip:
When solving systems of equations, elimination works well when the goal is to cancel out one variable by adding or subtracting the equations.

Solve the system of equations: 3x + 5y = 2 and x + 4y = -4.

Learn how to solve the system of equations 3x + 5y = 2 and x + 4y = -4 using both substitution and elimination methods. This problem covers key algebraic concepts such as the distributive property, properties of equality, and elimination. Suitable for students in Grades 9-10.

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