Sovi.AI - AI Math Tutor

Scan to solve math questions

QUESTION IMAGE

3. \\begin{cases} \\ \\ \\ y = 2x - 7 \\\\ \\ \\ \\ 4 + y = 12 \\end{ca…

Question

3.
\

$$\begin{cases} \\ \\ \\ y = 2x - 7 \\\\ \\ \\ \\ 4 + y = 12 \\end{cases}$$
step:step 2:check:

Explanation:

Step1: Solve for $y$

$4 + y = 12$
$y = 12 - 4$
$y = 8$

Step2: Substitute $y$ to find $x$

$y = 2x - 7$
$8 = 2x - 7$
$2x = 8 + 7$
$2x = 15$
$x = \frac{15}{2} = 7.5$

Step3: Verify solutions

Substitute $x=7.5$ and $y=8$ into both equations:

  1. $y = 2x - 7$: $8 = 2(7.5) - 7$ → $8 = 15 - 7$ → $8=8$ (True)
  2. $4 + y = 12$: $4 + 8 = 12$ → $12=12$ (True)

Answer:

$x = \frac{15}{2}$ (or $7.5$), $y = 8$