Solve the System of Equations: x - y = 8 and 3x + 2y = 24

xy=8 x-y=8

3x+2y=24 3x+2y=24

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's multiply one of the equations by 3, so we can subtract between them
00:14 Now let's subtract between the equations
00:21 Let's simplify what we can
00:29 Let's collect like terms
00:34 Let's isolate Y
00:38 This is the value of Y
00:43 Now let's substitute Y to find the value of X
00:50 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

xy=8 x-y=8

3x+2y=24 3x+2y=24

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Solve the first equation for one variable
  • Step 2: Substitute into the second equation
  • Step 3: Solve for the second variable
  • Step 4: Use this value to find the first variable

Now, let's work through each step:
Step 1: From the equation xy=8 x - y = 8 , solve for x x :

x=y+8 x = y + 8

Step 2: Substitute x=y+8 x = y + 8 into the second equation 3x+2y=24 3x + 2y = 24 .

3(y+8)+2y=24 3(y + 8) + 2y = 24

Simplify:
3y+24+2y=24 3y + 24 + 2y = 24

Combine like terms:
5y+24=24 5y + 24 = 24

Step 3: Solve for y y :

5y=2424 5y = 24 - 24

5y=0 5y = 0

y=0 y = 0

Step 4: Substitute y=0 y = 0 back into the expression for x x :

x=0+8 x = 0 + 8

x=8 x = 8

Therefore, the solution to the system of equations is x=8 x = 8 and y=0 y = 0 .

This matches choice 1.

3

Final Answer

x=8,y=0 x=8,y=0

Practice Quiz

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\( \begin{cases} x+y=8 \\ x-y=6 \end{cases} \)

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