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To solve this system, you could do the following steps:

3х + 4y = 48
6x + 2y = 60
(6 points)
1. Choose the best method to solve by looking at the way the equations are set up for you:
2. Using the best method, how could you get the x variables to cancel out?
3. After you complete step 2, what would your top equation be? !
4. Line them up and add the equations together to get this equation.
5. Solve for y.
6. Solve for x.
:: Substitution
Choose a method
:: Graphing
： Elimination
Operation to get the x variables to cancel
:: Multiply the bottom equation x 2
:: Divide the top equation by 4
:: Multiply the top equation x -2
:: Divide the bottom equation by 2
Simplified top equation
： ×+2y=46
:: -6x - 8y = -96
:: 3X + y = 30
:: -6x + 4y = 96
：-6y=-36
After adding the equations
：-8y=-96
：：8y =96
:: 6y = -96
：y=6
Solve for x and y
:: y=-12
： y=18
:: x=-3
： ×=6
：×=8

1 answer

Let's solve the system of equations step by step:

Given the equations:

  1. 3x + 4y = 48
  2. 6x + 2y = 60

Step 1: Choose the best method

To decide the best method, we can look at the coefficients and how to easily eliminate one variable. Since the second equation has a multiple of the first and is fairly straightforward to manipulate, we will use the elimination method.

Step 2: Operations to get the x variables to cancel

We can multiply the first equation by 2 to match the coefficient of x in the second equation:

  • Multiply the first equation by 2: \( 2(3x + 4y) = 2(48) \) Thus, \( 6x + 8y = 96 \)

Step 3: Simplify the top equation

The top equation after multiplying becomes:

  • \( 6x + 8y = 96 \)

Now we have the modified system of equations:

  1. \( 6x + 8y = 96 \) (modified first equation)
  2. \( 6x + 2y = 60 \) (original second equation)

Step 4: Align and subtract the equations

Now, let's subtract the second equation from the first to eliminate \( x \):

\[ (6x + 8y) - (6x + 2y) = 96 - 60 \] This simplifies to: \[ 6y = 36 \]

Step 5: Solve for y

Now, divide both sides by 6: \[ y = 6 \]

Step 6: Solve for x

Now, substitute \( y = 6 \) back into one of the original equations. Using the first equation: \[ 3x + 4(6) = 48 \] \[ 3x + 24 = 48 \] Subtract 24 from both sides: \[ 3x = 24 \] Now, divide by 3: \[ x = 8 \]

Final Solution:

The solution to the system of equations is:

  • \( x = 8 \)
  • \( y = 6 \)

So the solution is \( (x, y) = (8, 6) \).