Question

semester 1: unit 2 exam review

1. solve the system of equations and verify by substitution:

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$$\begin{cases} 2y = x - 4 \\\\ 4x + 2y = 6 \\end{cases}$$

(show all work)
priority standard: hsa.rei.c.6 – solve systems of linear equations.

Explanation:

Step1: Isolate $x$ from first equation

From $2y = x - 4$, rearrange to get:
$x = 2y + 4$

Step2: Substitute $x$ into second equation

Replace $x$ in $4x + 2y = 6$:
$4(2y + 4) + 2y = 6$
Expand and simplify:
$8y + 16 + 2y = 6$
$10y + 16 = 6$

Step3: Solve for $y$

Subtract 16 from both sides, then divide by 10:
$10y = 6 - 16 = -10$
$y = \frac{-10}{10} = -1$

Step4: Substitute $y=-1$ to find $x$

Use $x = 2y + 4$:
$x = 2(-1) + 4 = -2 + 4 = 2$

Step5: Verify solutions in both equations

First equation: $2y = x - 4$
Left side: $2(-1) = -2$; Right side: $2 - 4 = -2$ (matches)
Second equation: $4x + 2y = 6$
Left side: $4(2) + 2(-1) = 8 - 2 = 6$; Right side: $6$ (matches)

Answer:

$x=2$, $y=-1$