Question

solve each system of equations. see examples 1 and\

1. $x - y = 4$\

$2x + y = 5$\

1. $x - 2y = -2$\

$3x + 2y = 30$\

1. $3x + 2y = 8$\

$x + 4y = -4$\

1. $x - 2y = 1$\

$2x + 3y = -12$\

1. $7x - 4y = -12$\

$x - 2y = 4$\

1. $5x + 6y = -6$\

$7x - 3y = -54$\

1. $2x + 5y = -20$\

$3x - 2y = -11$\

1. $4x - 3y = 17$\

$2x - 5y = 5$

Explanation:

Problem 15

Step1: Add equations to eliminate $y$

$x - y + 2x + y = 4 + 5$
$3x = 9$

Step2: Solve for $x$

$x = \frac{9}{3} = 3$

Step3: Substitute $x=3$ into $x-y=4$

$3 - y = 4$
$y = 3 - 4 = -1$

Step1: Add equations to eliminate $y$

$x - 2y + 3x + 2y = -2 + 30$
$4x = 28$

Step2: Solve for $x$

$x = \frac{28}{4} = 7$

Step3: Substitute $x=7$ into $x-2y=-2$

$7 - 2y = -2$
$-2y = -2 -7 = -9$
$y = \frac{-9}{-2} = \frac{9}{2}$

Step1: Multiply first equation by 2

$2(3x + 2y) = 2\times8$
$6x + 4y = 16$

Step2: Subtract second equation

$6x + 4y - (x + 4y) = 16 - (-4)$
$5x = 20$

Step3: Solve for $x$

$x = \frac{20}{5} = 4$

Step4: Substitute $x=4$ into $x+4y=-4$

$4 + 4y = -4$
$4y = -8$
$y = -2$

Answer:

$x=3$, $y=-1$

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Problem 16