Question was provided via image upload.

Question

Accepted Answer

### Problem 1: Solve $\begin{cases}-v + w = 7\v + w = 1\end{cases}$
# Explanation:
## Step1: Eliminate $v$ by adding equations
Add the two equations: $(-v + w)+(v + w)=7 + 1$
Simplify: $-v + w+v + w = 8$ → $2w = 8$
## Step2: Solve for $w$
Divide both sides by 2: $w=\frac{8}{2}=4$
## Step3: Substitute $w = 4$ into $v + w = 1$
$v+4 = 1$
Subtract 4: $v=1 - 4=-3$
# Answer: $v=-3,w = 4$

### Problem 2: Solve $\begin{cases}y + z = 4\y - z = 8\end{cases}$
# Explanation:
## Step1: Eliminate $z$ by adding equations
Add the two equations: $(y + z)+(y - z)=4 + 8$
Simplify: $y + z+y - z = 12$ → $2y = 12$
## Step2: Solve for $y$
Divide by 2: $y=\frac{12}{2}=6$
## Step3: Substitute $y = 6$ into $y + z = 4$
$6+z = 4$
Subtract 6: $z=4 - 6=-2$
# Answer: $y = 6,z=-2$

### Problem 3: Solve $\begin{cases}-4x + 5y = 17\4x + 6y = -6\end{cases}$
# Explanation:
## Step1: Eliminate $x$ by adding equations
Add the two equations: $(-4x + 5y)+(4x + 6y)=17+(-6)$
Simplify: $-4x + 5y+4x + 6y = 11$ → $11y = 11$
## Step2: Solve for $y$
Divide by 11: $y=\frac{11}{11}=1$
## Step3: Substitute $y = 1$ into $4x + 6y = -6$
$4x+6(1)=-6$ → $4x+6=-6$
Subtract 6: $4x=-12$
Divide by 4: $x=\frac{-12}{4}=-3$
# Answer: $x=-3,y = 1$

### Problem 4: Solve $\begin{cases}5m - 2p = 24\3m + 2p = 24\end{cases}$
# Explanation:
## Step1: Eliminate $p$ by adding equations
Add the two equations: $(5m - 2p)+(3m + 2p)=24 + 24$
Simplify: $5m - 2p+3m + 2p = 48$ → $8m = 48$
## Step2: Solve for $m$
Divide by 8: $m=\frac{48}{8}=6$
## Step3: Substitute $m = 6$ into $3m + 2p = 24$
$3(6)+2p = 24$ → $18+2p = 24$
Subtract 18: $2p = 6$
Divide by 2: $p = 3$
# Answer: $m = 6,p = 3$

### Problem 5: Solve $\begin{cases}a + 4b = -4\a + 10b = -16\end{cases}$
# Explanation:
## Step1: Eliminate $a$ by subtracting equations
Subtract the first equation from the second: $(a + 10b)-(a + 4b)=-16-(-4)$
Simplify: $a + 10b-a - 4b=-12$ → $6b=-12$
## Step2: Solve for $b$
Divide by 6: $b=\frac{-12}{6}=-2$
## Step3: Substitute $b = -2$ into $a + 4b = -4$
$a+4(-2)=-4$ → $a-8=-4$
Add 8: $a = 4$
# Answer: $a = 4,b=-2$

### Problem 6: Solve $\begin{cases}6r - 6t = 6\3r - 6t = 15\end{cases}$
# Explanation:
## Step1: Eliminate $t$ by subtracting equations
Subtract the second equation from the first: $(6r - 6t)-(3r - 6t)=6 - 15$
Simplify: $6r - 6t-3r + 6t=-9$ → $3r=-9$
## Step2: Solve for $r$
Divide by 3: $r=\frac{-9}{3}=-3$
## Step3: Substitute $r = -3$ into $6r - 6t = 6$
$6(-3)-6t = 6$ → $-18-6t = 6$
Add 18: $-6t = 24$
Divide by -6: $t=-4$
# Answer: $r=-3,t=-4$

### Problem 7: Solve $\begin{cases}y=-4x + 11\3x + y = 9\end{cases}$
# Explanation:
## Step1: Substitute $y=-4x + 11$ into $3x + y = 9$
$3x+(-4x + 11)=9$
Simplify: $3x-4x + 11 = 9$ → $-x+11 = 9$
## Step2: Solve for $x$
Subtract 11: $-x=9 - 11=-2$
Multiply by -1: $x = 2$
## Step3: Substitute $x = 2$ into $y=-4x + 11$
$y=-4(2)+11=-8 + 11 = 3$
# Answer: $x = 2,y = 3$

### Problem 8: Solve $\begin{cases}y=-3x + 1\2x + y = 1\end{cases}$
# Explanation:
## Step1: Substitute $y=-3x + 1$ into $2x + y = 1$
$2x+(-3x + 1)=1$
Simplify: $2x-3x + 1 = 1$ → $-x+1 = 1$
## Step2: Solve for $x$
Subtract 1: $-x=1 - 1=0$
Multiply by -1: $x = 0$
## Step3: Substitute $x = 0$ into $y=-3x + 1$
$y=-3(0)+1 = 1$
# Answer: $x = 0,y = 1$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: Solve \(

Step1: Eliminate \(v\) by adding equations

Step2: Solve for \(w\)

Step3: Substitute \(w = 4\) into \(v + w = 1\)

Step1: Eliminate \(z\) by adding equations

Step2: Solve for \(y\)

Step3: Substitute \(y = 6\) into \(y + z = 4\)

Step1: Eliminate \(x\) by adding equations

Step2: Solve for \(y\)

Step3: Substitute \(y = 1\) into \(4x + 6y = -6\)

Answer:

Problem 2: Solve \(