Question

elijah gonzalez - copy of systems_of_equations_word_search file edit view insert format data tools extensions help 100% $ % .0 .00 123 centu... e11 a b c d e f g h 6 1 \

$$\begin{cases}4y = 9x + 16 \\\\ x = 3y + 11 \\end{cases}$$

7 2 \

$$\begin{cases}3x - 2y = 8 \\\\ 3x + y = 14 \\end{cases}$$

8 3 \

$$\begin{cases} y = 7x - 9 \\\\ y = -12x + 10 \\end{cases}$$

9 4 \

$$\begin{cases}10x - 5y = 25 \\\\ -2x - 5y = 1 \\end{cases}$$

10 5 \

$$\begin{cases}3y - 7x = 6 \\\\ y = 5x + 2 \\end{cases}$$

11 6 \

$$\begin{cases}y = -4x + 12 \\\\ y = 7x - 10 \\end{cases}$$

12 7 \

$$\begin{cases}6x - 2y = 46 \\\\ 5x - 6y = -5 \\end{cases}$$

(-x - 5y = 7

Explanation:

Let's solve the system of equations for problem 6:

$$\begin{cases} y = -4x + 12 \\ y = 7x - 10 \end{cases}$$

Step1: Set the two equations equal

Since both expressions equal $y$, we can set them equal to each other:
$-4x + 12 = 7x - 10$

Step2: Solve for $x$

Add $4x$ to both sides:
$12 = 11x - 10$
Add 10 to both sides:
$22 = 11x$
Divide both sides by 11:
$x = 2$

Step3: Solve for $y$

Substitute $x = 2$ into one of the original equations, say $y = -4x + 12$:
$y = -4(2) + 12$
$y = -8 + 12$
$y = 4$

Answer:

The solution is $x = 2$, $y = 4$ (or the ordered pair $(2, 4)$)