Absolutely! We can solve for x and y in the system of equations:
3x + 2y = 4
2x - 3y = 7
using elimination. Here's how:
* Look for an easy elimination: Notice that the coefficients of x in both equations are relatively close (3 and 2). This makes elimination efficient.
* Make the coefficients equal (optional): In this case, multiplying the top equation by -2 keeps the right side consistent and simplifies the elimination further:
-6x - 4y = -8 (Multiply top equation by -2)
2x - 3y = 7
* Eliminate y: Add the top and bottom equations.
-4x - 7y = -1
* Solve for x: Isolate x by dividing both sides by its coefficient:
-4x = -1
x = 1/4
* Solve for y: Substitute the value of x back into either of the original equations. We'll use the top equation here:
3 * (1/4) + 2y = 4
3/4 + 2y = 4
2y = 13/4
y = 13 / (2 * 4)
y = 13/8
Therefore, the solution is:
* x = 1/4
* y = 13/8
