Solve the system of equations. −6x+2y=−32 4x+3y=−9 (1 point) (, )

Answer 1

To solve the system of equations, we can use the substitution method or the elimination method.

Let's use the elimination method.

Multiply the first equation by 2 to eliminate y:

-12x + 4y = -64

Now, add the two equations:

-12x + 4y = -64
4x + 3y = -9

-8x + 7y = -73

Now, solve for y:

7y = 8x - 73
y = (8/7)x - 73/7

Now, substitute the expression for y back into the first equation and solve for x:

-6x + 2((8/7)x - 73/7) = -32
-6x + (16/7)x - 146/7 = -32
(-42/7)x + (16/7)x = 146/7 - 32
(-26/7)x = 146/7 - 224/7
(-26/7)x = -78/7
x = 3

Now, substitute x = 3 back into the expression for y and solve for y:

y = (8/7)(3) - 73/7
y = 24/7 - 73/7
y = -49/7

Therefore, the solution to the system of equations is (3, -49/7).

Answer 2

The Math Club sold slices of pizza, p , at a profit of $3 each and cans of soda, s , at $2 each to raise money for a trip. They sold 200 items and made a profit of $550. Write the pair of linear equations that model this situation.(1 point) Equation to represent the total number of items sold: = 200 Equation to represent the total profit: = 550

Answer 3

Let's represent the number of slices of pizza sold as p and the number of cans of soda sold as s.

1. Equation to represent the total number of items sold:
p + s = 200

This equation represents the fact that the total number of items sold (slices of pizza and cans of soda) is 200.

2. Equation to represent the total profit:
3p + 2s = 550

This equation represents the fact that the profit made from selling each slice of pizza at a profit of $3 and each can of soda at $2 totals $550.

Therefore, the pair of linear equations that model this situation is:
p + s = 200
3p + 2s = 550