Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for y. Assume the equation has a solution for y. {:[py+7=6y+q],[y=◻+=^(+)]:}

Solve for y y .\newlineAssume the equation has a solution for y y .\newlinepy+7=6y+qy=□ \begin{array}{l} p y+7=6 y+q \\ y=\square \end{array}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Rearrange multi-variable equationsright chevron icon

Full solution

Q. Solve for y y .\newlineAssume the equation has a solution for y y .\newlinepy+7=6y+qy=□ \begin{array}{l} p y+7=6 y+q \\ y=\square \end{array}
  1. Identify the system: Identify the system of equations to solve for yy.\newlineThe system is:\newline11. py+7=6y+qp y + 7 = 6 y + q\newline22. y=?y = ?\newlineWe need to isolate yy in the first equation.
  2. Subtract py py from both sides: Subtract py py from both sides of the equation to move all terms containing y y to one side.\newline(py+7)−py=(6y+q)−py (py + 7) - py = (6y + q) - py \newlineThis simplifies to:\newline7=6y−py+q 7 = 6y - py + q
  3. Factor out y from the terms: Factor out y from the terms on the right-hand side.\newline77 = y(66 - p) + q\newlineNow we have y multiplied by (66 - p) and an additional q on the right-hand side.
  4. Subtract qq from both sides: Subtract qq from both sides to isolate the term with yy.\newline7−q=y(6−p)7 - q = y(6 - p)\newlineNow we have y(6−p)y(6 - p) on one side and 7−q7 - q on the other side.
  5. Divide both sides by (6−p)(6 - p): Divide both sides by (6−p)(6 - p) to solve for yy.7−q6−p=y\frac{7 - q}{6 - p} = yThis gives us the value of yy in terms of pp and qq.

More problems from Rearrange multi-variable equations

Question
Solve for x. \newline(34)x=12(\frac{3}{4})x= 12 \newlinex=x = ______
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve for x. \newline−59x=15-\frac{5}{9}x= 15 \newlinex=x = ______
Get tutor helpright-arrow

Posted 7 months ago

Question
How many solutions does the following equation have?\newline5x+8−7x=−4x+15x+8-7x=-4x+1\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 10 months ago

Question
How many solutions does the following equation have?\newline−2z+10+7z=16z+7-2z+10+7z=16z+7\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 5 months ago

Question
How many solutions does the following equation have?\newline7(y−8)=7y+427(y-8)=7y+42\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 10 months ago

Question
How many solutions does the following equation have?\newline−9(x+6)=−9x+108-9(x+6)=-9x+108\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 10 months ago

Question
How many solutions does the following equation have?\newline−6(x+7)=−4x−2-6(x+7)=-4x-2\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 10 months ago

Question
How many solutions does the following equation have?\newline−4x−7+10x=−7+6x-4x-7+10x=-7+6x\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 10 months ago

Question
How many solutions does the following equation have?\newline−17(y−2)=−17y+64-17(y-2)=-17y+64\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 10 months ago

Question
How many solutions does the following equation have?\newline9z−6+7z=16z−69z-6+7z=16z-6\newlineChoose 11 answer:\newline(A) No solutions\newline(B) Exactly one solution\newline(C) Infinitely many solutions
Get tutor helpright-arrow

Posted 10 months ago

View all (50)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant