Question

solve each system of equations by substitution(examples 1-5)1. $y = x - 14LXB0x - yLXB1y = 6x + 5$5. $y =LXB2-x + 2y = 8$8.

Explanation:

Step1: Solve system 1 via substitution

Substitute $y = x - 14$ into $y = -6x$:
$$x - 14 = -6x$$
Add $6x$ to both sides:
$$7x - 14 = 0$$
Add 14 to both sides:
$$7x = 14$$
Divide by 7:
$$x = 2$$
Substitute $x=2$ into $y=-6x$:
$$y = -6(2) = -12$$

Step2: Solve system 4 via substitution

Substitute $y = 6x + 5$ into $y - 6x = 12$:
$$(6x + 5) - 6x = 12$$
Simplify left side:
$$5 = 12$$

Step3: Solve system 7 via substitution

First, solve $-x + 2y = 8$ for $x$:
$$x = 2y - 8$$
Substitute $x = 2y - 8$ into $-3x + 4y = 6$:
$$-3(2y - 8) + 4y = 6$$
Expand the left side:
$$-6y + 24 + 4y = 6$$
Combine like terms:
$$-2y + 24 = 6$$
Subtract 24 from both sides:
$$-2y = -18$$
Divide by -2:
$$y = 9$$
Substitute $y=9$ into $x=2y-8$:
$$x = 2(9) - 8 = 10$$

Answer:

1. $x=2$, $y=-12$
2. No solution (the equation $5=12$ is a contradiction)
3. $x=10$, $y=9$