Question

3x-4y=19. 6x 9y=21

Use elimination

Answer 1

The solution to the system of equations 3x - 4y = 19 and 6x + 9y = 21 using elimination is x = 5 and y = -1. This was achieved by multiplying the first equation by 2 and subtracting the second equation from it to eliminate x.

Step-by-step explanation:

The system of equations presented is:

• 3x - 4y = 19
• 6x + 9y = 21

To solve the system using elimination, we want to eliminate one of the variables (either x or y) by combining the two equations. This typically involves multiplying one or both of the equations by certain numbers to make the coefficients of one of the variables the same with opposite signs.

Looking at the coefficients of x and y, if we multiply the first equation by 2, we get:

• 6x - 8y = 38

Now, we have the first variable x with the same coefficient in both equations but with different signs:

• 6x - 8y = 38
• 6x + 9y = 21

By subtracting the second equation from the first, we can eliminate x and find the value of y:

1. (6x - 8y) - (6x + 9y) = 38 - 21
2. -17y = 17
3. y = 17 / -17
4. y = -1

With the value of y found, substitute it back into one of the original equations to find x:

1. 3x - 4(-1) = 19
2. 3x + 4 = 19
3. 3x = 19 - 4
4. 3x = 15
5. x = 15 / 3
6. x = 5

The solution to the system of equations is x = 5 and y = -1.