substitute the given value of x into the equation. then solve the equation for y.
1. ( 7x - 3y = 6; x = 3 )
2. ( 6x + 5y = -7; x = -2 )
3. ( xy = 12 + 3x; x = 4 )
4. ( \frac{2}{3}x = 2y - \frac{2}{5}; x = -9 )
5. ( \frac{2}{3}y + \frac{1}{2}x = 1; x = 12 )
6. ( x - 2y = 3xy + 1; x = -2 )

solve the equation for y. then find the value of y for the given value of x.
7. ( 3x - 6y = 6; x = 2 )
8. ( -2x + 2 = 5y - 1; x = 5 )
9. ( 2xy + 1 = xy + 3; x = 2 )
10. ( \frac{1}{2}x - y = \frac{3}{2}x - 3; x = 7 )
11. ( \frac{3}{4}x + \frac{4}{7}y = \frac{5}{4}x - 1; x = 8 )
12. ( \frac{3}{5}y - 4x = 3 - 2y; x = 9 )

solve the formula for the indicated variable.
13. fahrenheit to celsius
solve for ( f ): ( c = \frac{5}{9}(f - 32) )
14. perimeter of a parallelogram
solve for ( b ): ( p = 2b + 2s )
15. perimeter of a triangle
solve for ( c ): ( p = a + b + c )
16. area of a rhombus
solve for ( d_1 ): ( a = \frac{1}{2}d_1d_2 )

Question

substitute the given value of x into the equation. then solve the equation for y.
1. ( 7x - 3y = 6; x = 3 )
2. ( 6x + 5y = -7; x = -2 )
3. ( xy = 12 + 3x; x = 4 )
4. ( \frac{2}{3}x = 2y - \frac{2}{5}; x = -9 )
5. ( \frac{2}{3}y + \frac{1}{2}x = 1; x = 12 )
6. ( x - 2y = 3xy + 1; x = -2 )

solve the equation for y. then find the value of y for the given value of x.
7. ( 3x - 6y = 6; x = 2 )
8. ( -2x + 2 = 5y - 1; x = 5 )
9. ( 2xy + 1 = xy + 3; x = 2 )
10. ( \frac{1}{2}x - y = \frac{3}{2}x - 3; x = 7 )
11. ( \frac{3}{4}x + \frac{4}{7}y = \frac{5}{4}x - 1; x = 8 )
12. ( \frac{3}{5}y - 4x = 3 - 2y; x = 9 )

solve the formula for the indicated variable.
13. fahrenheit to celsius
solve for ( f ): ( c = \frac{5}{9}(f - 32) )
14. perimeter of a parallelogram
solve for ( b ): ( p = 2b + 2s )
15. perimeter of a triangle
solve for ( c ): ( p = a + b + c )
16. area of a rhombus
solve for ( d_1 ): ( a = \frac{1}{2}d_1d_2 )

Accepted Answer

### Problem 1: $ 7x - 3y = 6; x = 3 $
# Explanation:
## Step 1: Substitute $ x = 3 $ into the equation
Substitute $ x = 3 $ into $ 7x - 3y = 6 $, we get $ 7\times3 - 3y = 6 $, which simplifies to $ 21 - 3y = 6 $.
## Step 2: Solve for $ y $
Subtract 21 from both sides: $ -3y = 6 - 21 $, so $ -3y = -15 $. Then divide both sides by -3: $ y=\frac{-15}{-3}=5 $.
# Answer: $ y = 5 $

### Problem 2: $ 6x + 5y = -7; x = -2 $
# Explanation:
## Step 1: Substitute $ x = -2 $
Substitute $ x = -2 $ into $ 6x + 5y = -7 $, we have $ 6\times(-2)+5y=-7 $, that is $ -12 + 5y = -7 $.
## Step 2: Solve for $ y $
Add 12 to both sides: $ 5y=-7 + 12 $, so $ 5y = 5 $. Divide by 5: $ y = 1 $.
# Answer: $ y = 1 $

### Problem 3: $ xy=12 + 3x; x = 4 $
# Explanation:
## Step 1: Substitute $ x = 4 $
Substitute $ x = 4 $ into $ xy=12 + 3x $, we get $ 4y=12+3\times4 $.
## Step 2: Simplify and solve for $ y $
Simplify the right - hand side: $ 4y=12 + 12=24 $. Divide both sides by 4: $ y = 6 $.
# Answer: $ y = 6 $

### Problem 4: $ \frac{2}{3}x=2y-\frac{2}{5};x = - 9 $
# Explanation:
## Step 1: Substitute $ x=-9 $
Substitute $ x = - 9 $ into $ \frac{2}{3}x=2y-\frac{2}{5} $, we have $ \frac{2}{3}\times(-9)=2y-\frac{2}{5} $.
## Step 2: Simplify the left - hand side
$ \frac{2}{3}\times(-9)=-6 $, so the equation becomes $ -6=2y-\frac{2}{5} $.
## Step 3: Solve for $ y $
Add $ \frac{2}{5} $ to both sides: $ 2y=-6+\frac{2}{5}=\frac{-30 + 2}{5}=\frac{-28}{5} $. Divide both sides by 2: $ y=\frac{-28}{5}\div2=\frac{-28}{5}\times\frac{1}{2}=-\frac{14}{5}=-2.8 $.
# Answer: $ y =-\frac{14}{5} $ (or $ y=-2.8 $)

### Problem 5: $ \frac{2}{3}y+\frac{1}{2}x = 1;x = 12 $
# Explanation:
## Step 1: Substitute $ x = 12 $
Substitute $ x = 12 $ into $ \frac{2}{3}y+\frac{1}{2}x = 1 $, we get $ \frac{2}{3}y+\frac{1}{2}\times12 = 1 $.
## Step 2: Simplify the equation
$ \frac{1}{2}\times12 = 6 $, so the equation is $ \frac{2}{3}y+6 = 1 $.
## Step 3: Solve for $ y $
Subtract 6 from both sides: $ \frac{2}{3}y=1 - 6=-5 $. Multiply both sides by $ \frac{3}{2} $: $ y=-5\times\frac{3}{2}=-\frac{15}{2}=-7.5 $.
# Answer: $ y =-\frac{15}{2} $ (or $ y=-7.5 $)

### Problem 6: $ x - 2y=3xy + 1;x=-2 $
# Explanation:
## Step 1: Substitute $ x=-2 $
Substitute $ x = - 2 $ into $ x - 2y=3xy + 1 $, we have $ -2-2y=3\times(-2)y + 1 $.
## Step 2: Simplify the equation
Simplify the right - hand side: $ -2-2y=-6y + 1 $.
## Step 3: Solve for $ y $
Add $ 6y $ to both sides: $ -2 + 4y=1 $. Add 2 to both sides: $ 4y=3 $. Divide by 4: $ y=\frac{3}{4} $.
# Answer: $ y=\frac{3}{4} $

### Problem 7: $ 3x - 6y = 6;x = 2 $
# Explanation:
## Step 1: Solve the equation for $ y $
First, isolate the term with $ y $: $ -6y=6 - 3x $. Then divide both sides by -6: $ y=\frac{3x - 6}{6}=\frac{x - 2}{2} $.
## Step 2: Substitute $ x = 2 $
Substitute $ x = 2 $ into $ y=\frac{x - 2}{2} $, we get $ y=\frac{2 - 2}{2}=0 $.
# Answer: $ y = 0 $

### Problem 8: $ -2x + 2 = 5y-1;x = 5 $
# Explanation:
## Step 1: Solve the equation for $ y $
Isolate the term with $ y $: $ 5y=-2x + 2 + 1=-2x + 3 $. Then $ y=\frac{-2x + 3}{5} $.
## Step 2: Substitute $ x = 5 $
Substitute $ x = 5 $ into $ y=\frac{-2x + 3}{5} $, we have $ y=\frac{-2\times5+3}{5}=\frac{-10 + 3}{5}=-\frac{7}{5}=-1.4 $.
# Answer: $ y =-\frac{7}{5} $ (or $ y=-1.4 $)

### Problem 9: $ 2xy + 1=xy + 3;x = 2 $
# Explanation:
## Step 1: Solve the equation for $ y $
Subtract $ xy $ and 1 from both sides: $ 2xy-xy=3 - 1 $, so $ xy = 2 $, then $ y=\frac{2}{x}(x
eq0) $.
## Step 2: Substitute $ x = 2 $
Substitute $ x = 2 $ into $ y=\frac{2}{x} $, we get $ y=\frac{2}{2}=1 $.
# Answer: $ y = 1 $

### Problem 10: $ \frac{1}{2}x-y=\frac{3}{2}x - 3;x = 7 $
# Explanation:
## Step 1: Solve the equation for $ y $
Isolate $ y $: $ -y=\frac{3}{2}x-\frac{1}{2}x-3 $, $ -y=x - 3 $, so $ y=-x + 3 $.
## Step 2: Substitute $ x = 7 $
Substitute $ x = 7 $ into $ y=-x + 3 $, we get $ y=-7 + 3=-4 $.
# Answer: $ y=-4 $

### Problem 11: $ \frac{3}{4}x+\frac{4}{7}y=\frac{5}{4}x-1;x = 8 $
# Explanation:
## Step 1: Solve the equation for $ y $
Subtract $ \frac{3}{4}x $ from both sides: $ \frac{4}{7}y=\frac{5}{4}x-\frac{3}{4}x-1 $, $ \frac{4}{7}y=\frac{2}{4}x-1=\frac{1}{2}x-1 $. Multiply both sides by $ \frac{7}{4} $: $ y=\frac{7}{4}(\frac{1}{2}x - 1)=\frac{7}{8}x-\frac{7}{4} $.
## Step 2: Substitute $ x = 8 $
Substitute $ x = 8 $ into $ y=\frac{7}{8}x-\frac{7}{4} $, we have $ y=\frac{7}{8}\times8-\frac{7}{4}=7-\frac{7}{4}=\frac{28 - 7}{4}=\frac{21}{4}=5.25 $.
# Answer: $ y=\frac{21}{4} $ (or $ y = 5.25 $)

### Problem 12: $ \frac{3}{5}y-4x=3 - 2y;x = 9 $
# Explanation:
## Step 1: Solve the equation for $ y $
Add $ 2y $ and $ 4x $ to both sides: $ \frac{3}{5}y+2y=3 + 4x $. Combine like terms: $ \frac{3 + 10}{5}y=3 + 4x $, $ \frac{13}{5}y=3 + 4x $. Multiply both sides by $ \frac{5}{13} $: $ y=\frac{5(3 + 4x)}{13}=\frac{15 + 20x}{13} $.
## Step 2: Substitute $ x = 9 $
Substitute $ x = 9 $ into $ y=\frac{15 + 20x}{13} $, we get $ y=\frac{15+20\times9}{13}=\frac{15 + 180}{13}=\frac{195}{13}=15 $.
# Answer: $ y = 15 $

### Problem 13: Solve $ C=\frac{5}{9}(F - 32) $ for $ F $
# Explanation:
## Step 1: Multiply both sides by $ \frac{9}{5} $
$ \frac{9}{5}C=F - 32 $.
## Step 2: Add 32 to both sides
$ F=\frac{9}{5}C + 32 $.
# Answer: $ F=\frac{9}{5}C + 32 $

### Problem 14: Solve $ P = 2b+2s $ for $ b $
# Explanation:
## Step 1: Subtract $ 2s $ from both sides
$ P-2s = 2b $.
## Step 2: Divide both sides by 2
$ b=\frac{P - 2s}{2} $.
# Answer: $ b=\frac{P - 2s}{2} $

### Problem 15: Solve $ P=a + b + c $ for $ c $
# Explanation:
## Step 1: Subtract $ a $ and $ b $ from both sides
$ c=P - a - b $.
# Answer: $ c=P - a - b $

### Problem 16: Solve $ A=\frac{1}{2}d_1d_2 $ for $ d_1 $
# Explanation:
## Step 1: Multiply both sides by 2
$ 2A=d_1d_2 $.
## Step 2: Divide both sides by $ d_2(d_2
eq0) $
$ d_1=\frac{2A}{d_2} $.
# Answer: $ d_1=\frac{2A}{d_2} $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: \( 7x - 3y = 6; x = 3 \)

Step 1: Substitute \( x = 3 \) into the equation

Step 2: Solve for \( y \)

Step 1: Substitute \( x = -2 \)

Step 2: Solve for \( y \)

Step 1: Substitute \( x = 4 \)

Step 2: Simplify and solve for \( y \)

Answer:

Problem 2: \( 6x + 5y = -7; x = -2 \)