Question

tuesday, february 3$^{rd}$ do now
find the solution using any method!
$y = -8x + 24$
$y = 6x - 4$

$y = 6x - 8$
$18x - 3y = 24$

$-4x + 8y = 28$
$4x - y = 14$

Explanation:

System 1: $y=-8x+24$; $y=6x-4$

Step1: Set equations equal

$-8x + 24 = 6x - 4$

Step2: Isolate $x$ terms

$-8x - 6x = -4 - 24$
$-14x = -28$

Step3: Solve for $x$

$x = \frac{-28}{-14} = 2$

Step4: Substitute $x=2$ to find $y$

$y = 6(2) - 4 = 12 - 4 = 8$

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System 2: $y=6x-8$; $18x-3y=24$

Step1: Substitute $y$ into second equation

$18x - 3(6x - 8) = 24$

Step2: Simplify left side

$18x - 18x + 24 = 24$
$24 = 24$

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System 3: $-4x+8y=28$; $4x-y=14$

Step1: Add equations to eliminate $x$

$(-4x + 8y) + (4x - y) = 28 + 14$

Step2: Simplify to solve for $y$

$7y = 42$
$y = \frac{42}{7} = 6$

Step3: Substitute $y=6$ to find $x$

$4x - 6 = 14$
$4x = 20$
$x = \frac{20}{4} = 5$

Answer:

1. For $y=-8x+24$ and $y=6x-4$: $x=2$, $y=8$
2. For $y=6x-8$ and $18x-3y=24$: Infinitely many solutions (the equations are equivalent)
3. For $-4x+8y=28$ and $4x-y=14$: $x=5$, $y=6$