The image presents a system of linear equations that you need to solve using the elimination method:

$3x + 2y = 3$ $2x + 3y = 2$

To use the elimination method, we aim to eliminate one of the variables by multiplying both equations by suitable numbers so that the coefficients of one of the variables match. Let's go through the solution step-by-step.

Step 1: Eliminate one variable

We can eliminate $x$ by making the coefficients of $x$ in both equations the same. To do this, we multiply the first equation by 2 and the second equation by 3.

• Multiply the first equation by 2: $2(3x + 2y) = 2(3)$ $6x + 4y = 6$

• Multiply the second equation by 3: $3(2x + 3y) = 3(2)$ $6x + 9y = 6$

Now, we have the system: $6x + 4y = 6$ $6x + 9y = 6$

Step 2: Subtract the equations

Next, subtract the first equation from the second to eliminate $x$: $(6x + 9y) - (6x + 4y) = 6 - 6$ $5y = 0$ $y = 0$

Step 3: Substitute $y = 0$ into one of the original equations

Now that we know $y = 0$, substitute this value into one of the original equations to solve for $x$. Let's use the first equation:

$3x + 2(0) = 3$ $3x = 3$ $x = 1$

Final Solution:

The solution is $x = 1$ and $y = 0$, or as an ordered pair:

$(1, 0)$

Would you like a further explanation or have any questions about this method?

Here are 5 related questions:

1. What would happen if we chose to eliminate $y$ instead of $x$?
2. Can the elimination method be used if the coefficients are already equal?
3. How does the substitution method differ from elimination when solving systems of equations?
4. What would the solution be if the system of equations had no solution?
5. How can we check the solution to a system of equations graphically?

Tip: When using the elimination method, always look for a quick way to make the coefficients of one variable the same (often by multiplying both equations).