Let's solve each system of equations using substitution.

Problem 1:

1. $y = 6 - x$
2. $4x - 3y = -4$

Substitute $y$ from equation 1 into equation 2: $4x - 3(6 - x) = -4$ $4x - 18 + 3x = -4$ $7x - 18 = -4$ $7x = 14$ $x = 2$

Now substitute $x$ back into equation 1 to find $y$: $y = 6 - 2$ $y = 4$

Solution: $x = 2$, $y = 4$

Problem 2:

1. $x = -y + 3$
2. $3x - 2y = -1$

Substitute $x$ from equation 1 into equation 2: $3(-y + 3) - 2y = -1$ $-3y + 9 - 2y = -1$ $-5y + 9 = -1$ $-5y = -10$ $y = 2$

Now substitute $y$ back into equation 1 to find $x$: $x = -2 + 3$ $x = 1$

Solution: $x = 1$, $y = 2$

Problem 3:

1. $-3x - y = 7$
2. $x + 2y = 6$

Solve equation 1 for $y$: $-y = 7 + 3x$ $y = -7 - 3x$

Substitute $y$ from this equation into equation 2: $x + 2(-7 - 3x) = 6$ $x - 14 - 6x = 6$ $-5x - 14 = 6$ $-5x = 20$ $x = -4$

Now substitute $x$ back into the equation for $y$: $y = -7 - 3(-4)$ $y = -7 + 12$ $y = 5$

Solution: $x = -4$, $y = 5$

Problem 4:

1. $6x - 3y = -6$
2. $y = 2x + 2$

Substitute $y$ from equation 2 into equation 1: $6x - 3(2x + 2) = -6$ $6x - 6x - 6 = -6$ $-6 = -6$

This indicates that the system has infinitely many solutions because the two equations are dependent.

Problem 5:

Write a system of equations for the total number of soccer balls and the total amount collected: $x + y = 70$ $65x + 15y = 2400$

Solve the first equation for $y$: $y = 70 - x$

Substitute $y$ into the second equation: $65x + 15(70 - x) = 2400$ $65x + 1050 - 15x = 2400$ $50x + 1050 = 2400$ $50x = 1350$ $x = 27$

Now substitute $x$ back into the first equation: $27 + y = 70$ $y = 43$

Solution: 27 Limited Edition soccer balls, 43 Pro NSL soccer balls.

Do you want more details or have any questions?

Related Questions:

1. How would you check the solutions obtained for each system of equations?
2. Can you solve each system of equations using the elimination method?
3. What are the key steps in solving a system of linear equations using substitution?
4. How can you verify if a system of equations has infinitely many solutions or no solutions?
5. Can you create and solve a system of equations for a different set of problems, similar to Problem 5?

Tip:

When solving systems of equations, always double-check your substitution and simplification steps to avoid errors.