What is the solution to this system of linear equations 2x + 3y = 3 and 7x + 3y = 24?

To solve the system of equations:

• Equation 1: 2x + 3y = 3
• Equation 2: 7x + 3y = 24

We can use the method of elimination or substitution. Here, we’ll use the elimination method:

1. First, we’ll multiply the first equation by 7 to align the coefficients of x in both equations:

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

14x + 21y = 21

2. Now we have the modified system:

• Modified Equation 1: 14x + 21y = 21
• Equation 2: 7x + 3y = 24

Next, we can multiply Equation 2 by 7 to align it with the modified Equation 1:

7(7x + 3y) = 7(24)

49x + 21y = 168

3. Now we subtract the modified Equation 1 from this new equation:

(49x + 21y) – (14x + 21y) = 168 – 21

35x = 147

4. Now solve for x:

x = 147 / 35

x = 4.2

5. Next, we substitute x back into one of the original equations, let’s use Equation 1:

2(4.2) + 3y = 3

8.4 + 3y = 3

6. Now solve for y:

3y = 3 – 8.4

3y = -5.4

y = -5.4 / 3

y = -1.8

So the solution to the system of equations is:

• x = 4.2
• y = -1.8

This means the point (4.2, -1.8) is the intersection of the two lines represented by the equations, making it the solution to the system.