Question

1. $-4x + y = 6$

$-5x - y = 21$

1. $-7x - 2y = -13$

$x - 2y = 11$

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

$-3x + 6y = -12$

1. $-5x + y = -3$

$3x - 8y = 24$

Explanation:

Problem 7:

Step1: Add the two equations

$$(-4x + y) + (-5x - y) = 6 + 21$$
$$-9x = 27$$

Step2: Solve for $x$

$$x = \frac{27}{-9} = -3$$

Step3: Substitute $x=-3$ into first equation

$$-4(-3) + y = 6$$
$$12 + y = 6$$

Step4: Solve for $y$

$$y = 6 - 12 = -6$$

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Problem 8:

Step1: Subtract the two equations

$$(-7x - 2y) - (x - 2y) = -13 - 11$$
$$-8x = -24$$

Step2: Solve for $x$

$$x = \frac{-24}{-8} = 3$$

Step3: Substitute $x=3$ into second equation

$$3 - 2y = 11$$
$$-2y = 11 - 3 = 8$$

Step4: Solve for $y$

$$y = \frac{8}{-2} = -4$$

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Problem 9:

Step1: Isolate $y$ from first equation

$$y = 5x - 2$$

Step2: Substitute $y=5x-2$ into second equation

$$-3x + 6(5x - 2) = -12$$
$$-3x + 30x - 12 = -12$$
$$27x - 12 = -12$$

Step3: Solve for $x$

$$27x = 0 \implies x = 0$$

Step4: Substitute $x=0$ into $y=5x-2$

$$y = 5(0) - 2 = -2$$

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Problem 10:

Step1: Isolate $y$ from first equation

$$y = 5x - 3$$

Step2: Substitute $y=5x-3$ into second equation

$$3x - 8(5x - 3) = 24$$
$$3x - 40x + 24 = 24$$
$$-37x + 24 = 24$$

Step3: Solve for $x$

$$-37x = 0 \implies x = 0$$

Step4: Substitute $x=0$ into $y=5x-3$

$$y = 5(0) - 3 = -3$$

Answer:

1. $x=-3$, $y=-6$
2. $x=3$, $y=-4$
3. $x=0$, $y=-2$
4. $x=0$, $y=-3$