Question

1. \\(2x - 3y = 24\\) \\(3x + 2y = -3\\) (\\(\underline{quad\quad}\\), \\(\underline{quad\quad}\\)) 11. \\(4x - 2y = -2\\) \\(-3x + 5y = 19\\) (\\(\underline{quad\quad}\\), \\(\underline{quad\quad}\\)) 12. \\(9x + 7y = 2\\) \\(2x + 8y = -6\\) (\\(\underline{quad\quad}\\), \\(\underline{quad\quad}\\))

Explanation:

Problem 10

Step1: Eliminate y, scale equations

Multiply first eq by 2: $4x - 6y = 48$
Multiply second eq by 3: $9x + 6y = -9$

Step2: Add equations to solve x

$4x - 6y + 9x + 6y = 48 + (-9)$
$13x = 39$
$x = \frac{39}{13} = 3$

Step3: Substitute x=3 to find y

$2(3) - 3y = 24$
$6 - 3y = 24$
$-3y = 24 - 6 = 18$
$y = \frac{18}{-3} = -6$

Step1: Simplify first equation

Divide $4x - 2y = -2$ by 2: $2x - y = -1$ → $y = 2x + 1$

Step2: Substitute y into second eq

$-3x + 5(2x + 1) = 19$
$-3x + 10x + 5 = 19$
$7x = 19 - 5 = 14$
$x = \frac{14}{7} = 2$

Step3: Substitute x=2 to find y

$y = 2(2) + 1 = 5$

Step1: Simplify second equation

Divide $2x + 8y = -6$ by 2: $x + 4y = -3$ → $x = -3 - 4y$

Step2: Substitute x into first eq

$9(-3 - 4y) + 7y = 2$
$-27 - 36y + 7y = 2$
$-29y = 2 + 27 = 29$
$y = \frac{29}{-29} = -1$

Step3: Substitute y=-1 to find x

$x = -3 - 4(-1) = -3 + 4 = 1$

Answer:

$(3, -6)$

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Problem 11