To solve this system, you could do the following steps: 3x+4y=48 6x+2y=60 (6 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. 1. Choose the best method to solve by looking at the way the equations are set up for you: Response area 2. Using the best method, how could you get the x variables to cancel out? Response area 3. After you complete step 2, what would your top equation be? Response area 4. Line them up and add the equations together to get this equation. Response area 5. Solve for y. Response area 6. Solve for x. Response area
1. Choose the best method to solve by looking at the way the equations are set up for you:
The best method to solve this system of equations is the method of elimination.
2. Using the best method, how could you get the x variables to cancel out?
To cancel out the x variables, you can multiply the first equation by 2 and the second equation by 3. This will make the coefficients of x in both equations equal.
3. After you complete step 2, what would your top equation be?
The top equation would be: 6x + 8y = 96.
4. Line them up and add the equations together to get this equation.
6x + 8y = 96 (from step 3)
+ 6x + 2y = 60
Adding the equations together, we get:
12x + 10y = 156
5. Solve for y.
To solve for y, we need to isolate y on one side of the equation. Subtracting 12x from both sides, we get:
10y = 156 - 12x
Dividing both sides by 10, we get:
y = (156 - 12x) / 10
6. Solve for x.
To solve for x, we can substitute the value of y from step 5 into any of the original equations. Let's substitute it into the second equation:
6x + 2((156 - 12x) / 10) = 60
Simplifying the equation, we get:
6x + (312 - 24x) / 10 = 60
Multiplying both sides by 10 to eliminate the fraction, we get:
60x + 312 - 24x = 600
Combining like terms, we get:
36x + 312 = 600
Subtracting 312 from both sides, we get:
36x = 288
Dividing both sides by 36, we get:
x = 8
So the solution to the system of equations is x = 8 and y = (156 - 12(8)) / 10, which simplifies to y = 3.
1. To choose the best method to solve the given system of equations, we can examine the coefficients of the x and y terms in both equations.
Looking at the first equation, 3x + 4y = 48, we see that the coefficients in front of x and y are 3 and 4, respectively.
In the second equation, 6x + 2y = 60, the coefficients in front of x and y are 6 and 2, respectively.
Since the x coefficients in both equations are different, the best method to eliminate x variables is by using the method of elimination or addition/subtraction.
2. To cancel out the x variables, we need to multiply one or both equations by suitable coefficients in order to make the x coefficients equal in magnitude but with opposite signs (one positive and one negative).
In this case, we can multiply the first equation by 2 and the second equation by -3. This will result in the x coefficients becoming -6 in both equations:
2(3x + 4y) = 2(48) --> 6x + 8y = 96
-3(6x + 2y) = -3(60) --> -18x - 6y = -180
3. After completing step 2, the top equation will be: 6x + 8y = 96.
4. To line up and add the equations together, we can stack them vertically:
6x + 8y = 96
-18x - 6y = -180
Adding the two equations together:
(6x + 8y) + (-18x - 6y) = 96 + (-180)
-12x + 2y = -84
So, the resulting equation is -12x + 2y = -84.
5. To solve for y, we can rearrange the equation -12x + 2y = -84 to isolate the y term:
2y = 12x - 84
Dividing both sides by 2:
y = 6x - 42
6. To solve for x, we need to substitute the value of y from step 5 into either of the original equations. Let's use the first equation, 3x + 4y = 48:
3x + 4(6x - 42) = 48
3x + 24x - 168 = 48
27x - 168 = 48
27x = 216
x = 8
Therefore, the solution to the given system of equations is x = 8 and y = 6x - 42 (which becomes y = 6(8) - 42 = 48 - 42 = 6).
1. Choose the best method to solve by looking at the way the equations are set up for you:
The given system of equations is in standard form, so one method to solve it is by using the method of elimination.
2. Using the best method, how could you get the x variables to cancel out?
To cancel out the x variables, you can multiply the first equation by 2 and the second equation by -3. This will result in the coefficients of the x-term being equal but with opposite signs.
3. After you complete step 2, what would your top equation be?
After multiplying the equations, the new top equation will be:
6x + 8y = 96
4. Line them up and add the equations together to get this equation.
Adding the modified equations together, you would get:
6x + 8y + 6x + 2y = 96 + 60
Simplifying this equation further, we have:
12x + 10y = 156
5. Solve for y.
To solve for y, we can use the equation: 12x + 10y = 156.
First, bring the 12x term to the other side:
10y = 156 - 12x
Next, divide both sides by 10:
y = (156 - 12x) / 10
6. Solve for x.
To solve for x, you can substitute the value of y found in the previous step into either of the original equations (let's choose the first equation).
Substituting y = (156 - 12x) / 10 into 3x + 4y = 48, we have:
3x + 4((156 - 12x) / 10) = 48
Now, simplify and solve for x:
Multiply both sides by 10 to eliminate the fraction:
30x + 4(156 - 12x) = 480
Distribute the 4:
30x + 624 - 48x = 480
Combine like terms:
-18x + 624 = 480
Subtract 624 from both sides:
-18x = -144
Divide both sides by -18:
x = 8
So the solution is x = 8.
To find the value of y, substitute this value of x back into either of the original equations:
Using the first equation, 3x + 4y = 48:
3(8) + 4y = 48
24 + 4y = 48
4y = 48 - 24
4y = 24
Divide both sides by 4:
y = 6
So the solution is y = 6.
Therefore, the solution to the given system of equations is x = 8 and y = 6.