To solve the system of equations by substitution, follow these steps:

Step 1: Substitute $x = 5y - 3$ into $3x - 2y = 4$.

The given equations are: $3x - 2y = 4$ $x = 5y - 3$

Substitute $x = 5y - 3$ into the first equation: $3(5y - 3) - 2y = 4$

Step 2: Simplify the equation.

Expand the terms: $15y - 9 - 2y = 4$ Combine like terms: $13y - 9 = 4$

Step 3: Solve for $y$.

Add 9 to both sides: $13y = 13$ Divide by 13: $y = 1$

Step 4: Solve for $x$ using $x = 5y - 3$.

Substitute $y = 1$ into $x = 5y - 3$: $x = 5(1) - 3$ $x = 5 - 3$ $x = 2$

Final Answer:

The solution is: $(x, y) = (2, 1)$

Would you like a detailed explanation of any step or additional examples?

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Related Questions:

1. How can substitution be applied to nonlinear systems of equations?
2. What are the advantages of substitution over elimination in solving systems?
3. How do we verify solutions to systems of equations?
4. What happens if a system of equations has no solution or infinitely many solutions?
5. Can substitution work for systems with three variables?

Tip:

Always substitute back the solution into the original equations to verify your results!