Question

13.3 activity check your answers on desmos graphing
solve each system without graphing.
\

$$\begin{cases} 5x - 2y = 26 \\\\ y + 4 = x \\end{cases}$$

\

$$\begin{cases} 2m - 2p = -6 \\\\ p = 2m + 10 \\end{cases}$$

\

$$\begin{cases} 2d = 8f \\\\ 18 - 4f = 2d \\end{cases}$$

\

$$\begin{cases} w + \\frac{1}{7}z = 4 \\\\ z = 3w - 2 \\end{cases}$$

Explanation:

---

System 1:

$$\begin{cases}5x-2y=26 \\ y+4=x\end{cases}$$

Step1: Substitute $x=y+4$

$5(y+4)-2y=26$

Step2: Expand and simplify

$5y+20-2y=26 \implies 3y=6$

Step3: Solve for $y$

$y=\frac{6}{3}=2$

Step4: Solve for $x$

$x=2+4=6$

---

System 2:

$$\begin{cases}2m-2p=-6 \\ p=2m+10\end{cases}$$

Step1: Substitute $p=2m+10$

$2m-2(2m+10)=-6$

Step2: Expand and simplify

$2m-4m-20=-6 \implies -2m=14$

Step3: Solve for $m$

$m=\frac{14}{-2}=-7$

Step4: Solve for $p$

$p=2(-7)+10=-14+10=-4$

---

System 3:

$$\begin{cases}2d=8f \\ 18-4f=2d\end{cases}$$

Step1: Substitute $2d=8f$

$18-4f=8f$

Step2: Combine like terms

$18=12f$

Step3: Solve for $f$

$f=\frac{18}{12}=\frac{3}{2}$

Step4: Solve for $d$

$2d=8\times\frac{3}{2}=12 \implies d=6$

---

System 4:

$$\begin{cases}w+\frac{1}{7}z=4 \\ z=3w-2\end{cases}$$

Step1: Substitute $z=3w-2$

$w+\frac{1}{7}(3w-2)=4$

Step2: Multiply through by 7

$7w+3w-2=28 \implies 10w=30$

Step3: Solve for $w$

$w=\frac{30}{10}=3$

Step4: Solve for $z$

$z=3(3)-2=9-2=7$

Answer:

1. $x=6,\ y=2$
2. $m=-7,\ p=-4$
3. $d=6,\ f=\frac{3}{2}$
4. $w=3,\ z=7$