To find the points where the system of equations intersect, let's solve the following system:

1. $x = y - 1$
2. $3x = 2y$

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

Since $x$ is already defined as $y - 1$ in the first equation, we can substitute this into the second equation:

$3(y - 1) = 2y$

Step 2: Solve for $y$

Expand and simplify the equation:

$3y - 3 = 2y$

Subtract $2y$ from both sides:

$y - 3 = 0$

$y = 3$

Step 3: Find $x$ using $y = 3$

Substitute $y = 3$ back into the first equation:

$x = 3 - 1$

$x = 2$

Solution

The solution is the point where the two lines intersect: $(x, y) = (2, 3)$

Would you like more details or have any questions about this solution?

Related Questions

1. How do you solve a system of equations using the substitution method?
2. What is the graphical interpretation of solving two linear equations?
3. How do you verify if a solution is correct for a system of equations?
4. How can you solve a system of equations using the elimination method?
5. What happens when a system of equations has no solution or infinitely many solutions?

Tip

Always double-check your substitution when solving equations to avoid mistakes in calculations!