Answer:

Certainly, here's the solution to the system of equations using the Gaussian elimination method step by step:

Given equations:

1. 3x - 2y = 7

2. 2x + 4y = 10

Step 1: Multiply equation (1) by 2 to make the coefficients of y cancel when added to equation (2):

2(3x - 2y) = 2(7)

6x - 4y = 14

Step 2: Now, you have the following system of equations:

1. 6x - 4y = 14

2. 2x + 4y = 10

Step 3: Add equation (2) to equation (1) to eliminate y:

(6x - 4y) + (2x + 4y) = 14 + 10

8x = 24

Step 4: Divide both sides by 8 to solve for x:

8x = 24

x = 24 / 8

x = 3

Step 5: Substitute the value of x into equation (1) to solve for y:

3x - 2y = 7

3(3) - 2y = 7

9 - 2y = 7

Step 6: Subtract 9 from both sides:

-2y = 7 - 9

-2y = -2

Step 7: Divide both sides by -2 to solve for y:

y = -2 / -2

y = 1

So, the solution to the system of equations is x = 3 and y = 1.