https://file.aiquickdraw.com/mathbot/file/1728951247295u4jxbe90.jpg

Let's solve the given system of equations by elimination:

\[
\begin{aligned}
5x - 5y &= -35 \quad \text{(Equation 1)} \\
-10x + 10y &= 70 \quad \text{(Equation 2)}
\end{aligned}
\]

### Step 1: Eliminate one variable
We notice that the coefficients of \(x\) and \(y\) in both equations are proportional. To eliminate one variable, we can add the two equations.

Let's multiply Equation 1 by 2 to align the coefficients of \(x\) and \(y\) with those in Equation 2:

\[
2(5x - 5y) = 2(-35) \implies 10x - 10y = -70
\]

So we now have:

\[
\begin{aligned}
10x - 10y &= -70 \quad \text{(Modified Equation 1)} \\
-10x + 10y &= 70 \quad \text{(Equation 2)}
\end{aligned}
\]

### Step 2: Add the equations
Now, add the two equations:

\[
(10x - 10y) + (-10x + 10y) = -70 + 70
\]

This simplifies to:

\[
0 = 0
\]

### Step 3: Interpretation
Since the result is a true statement (0 = 0), this indicates that the system of equations has **infinitely many solutions**. The two equations are dependent, meaning they represent the same line.

### Final Answer:
There is an **infinite number of solutions**.

Do you want more details or have any questions? Here are some related questions to deepen your understanding:

1. How do you recognize when a system has no solution?
2. Can two equations represent the same line even if their forms look different?
3. How would you graph these two equations to visually confirm the solution?
4. What does it mean when the system has exactly one solution?
5. How can substitution be used to solve this system of equations?

**Tip:** In elimination, always check if the equations are proportional. This often helps you recognize special cases like infinitely many or no solutions!

Solve the system of equations by elimination:
 5x - 5y = -35
 -10x + 10y = 70

Learn how to solve a system of linear equations using the elimination method with a detailed solution for 5x - 5y = -35 and -10x + 10y = 70. This problem covers key algebraic concepts like systems of linear equations and elimination. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation