You have the system of equations:

1. $7x - y = 34$
2. $2x + 3y = -10$

Let's solve this step by step.

Step 1: Solve one of the equations for one variable

We'll solve the first equation for $y$:

$7x - y = 34$ Add $y$ to both sides: $7x = y + 34$ Now subtract 34 from both sides: $y = 7x - 34$

Step 2: Substitute into the second equation

Now substitute $y = 7x - 34$ into the second equation $2x + 3y = -10$:

$2x + 3(7x - 34) = -10$ Expand the parentheses: $2x + 21x - 102 = -10$ Combine like terms: $23x - 102 = -10$ Add 102 to both sides: $23x = 92$ Now divide both sides by 23: $x = 4$

Step 3: Substitute $x = 4$ back into the first equation to find $y$

Substitute $x = 4$ into $y = 7x - 34$:

$y = 7(4) - 34$ $y = 28 - 34$ $y = -6$

Final Answer:

The solution is $x = 4$ and $y = -6$.

Would you like more detailed steps on solving systems of equations, or do you have any questions about the process?

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Here are some related questions:

1. How do you solve a system of equations using substitution?
2. What is the graphical method for solving systems of equations?
3. How would you solve the same system using the elimination method?
4. Can you solve a system of equations that has no solution?
5. How would you interpret a system of equations with infinitely many solutions?

Tip: When solving systems of equations, the substitution method is often easier when one of the equations is already solved for one variable.