The substitution method is a powerful technique for solving systems of equations. Here's a step-by-step guide:

Example Problem:

Solve the system of equations: $1) \; y = 2x + 3$ $2) \; 3x - y = -2$

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Steps:

1. Isolate one variable in one of the equations (already done in equation $y = 2x + 3$).

2. Substitute the expression for the isolated variable into the other equation.
   From Equation (1), substitute $y = 2x + 3$ into Equation (2): $3x - (2x + 3) = -2$

3. Simplify and solve for the remaining variable: $3x - 2x - 3 = -2$ $x - 3 = -2$ $x = 1$

4. Back-substitute the value of $x$ into the first equation ($y = 2x + 3$) to solve for $y$: $y = 2(1) + 3$ $y = 5$

5. Write the solution as a pair: $\boxed{(x, y) = (1, 5)}$

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Verify the Solution:

Substitute $x = 1$ and $y = 5$ into the second equation: $3(1) - 5 = -2$ Correct! Thus, the solution is valid.

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Would you like further details or another example? Let me know! Here are 5 related questions:

1. Can you solve a system of three equations using substitution?
2. What happens if the system has no solution or infinitely many solutions?
3. How does substitution compare to the elimination method?
4. Can substitution work for nonlinear systems of equations?
5. How can you use substitution when fractions are involved?

Tip:

Always simplify the equations as much as possible before substituting to reduce calculation errors.