What is the solution tot his system of linear equations 2x + 3y = 3 7x - 3y = 24

The solution for this system is x = 3 and y = - 1.

Step-by-step explanation:

1. Let's solve the system of equations to find out the value of x and y:

1st equation:

2x + 3y = 3

2x = 3 - 3y (Subtracting 3y at both sides)

x = 3/2 - 3y/2 (Dividing by 2 at both sides)

2nd equation:

7x - 3y = 24

Replacing x with the result of the 1st equation:

7 (3/2 - 3y/2) - 3y = 24

21/2 - 21y/2 - 3y = 24

- 21y/2 - 3y = 24 - 21/2 (Subtracting 21/2 at both sides)

-21y - 6y = 48 - 21 (Multiplying by 2 at both sides)

- 27y = 27

y = - 1 (Dividing by - 27 at both sides)

Now we can find out the value of x:

2x + 3y = 3

2x + 3 (-1) = 3

2x - 3 = 3

2x = 6 (Adding 6 at both sides)

x = 3 (Dividing by 2 at both sides)

3. Let's prove that x = 3 and y = - 1 are correct in the 2nd equation:

7x - 3y = 24

7 (3) - 3 (-1) = 24

21 + 3 = 24

24 = 24

We proved that x = 3 and y = - 1 are correct.