sorry this was all that was given. you have to choose one ore the other
To solve this system, you could do the following steps:
3x+4y=48
6x+2y=60
Choose the best method to solve by looking at the way the equations are set up for you:
Using the best method, how could you get the x variables to cancel out?
. After you complete step 2, what would your top equation be? Response area
Line them up and add the equations together to get this equation.
. Solve for y.
. Solve for x.
all the possible solutions:
choose a method:
substitution, graphing, elimination
Operation to get the x variables to cancel
divide the bottom equation by 2
multiply the bottom equation by x2
mulitply the top equation by x-2
divide the top equation by 4
simplified top equation
-6x+4y=96
x+2y=46
-6x-8y=-96
3x+7=30
after adding the equations
8y-96
-6y=-36
6y=-96
-8y=-96
solve for x and y
y=-12
x=6
y=18
x=-3
The best method to solve this system is elimination.
To get the x variables to cancel out, you would multiply the top equation by -2.
After completing step 2, the top equation would be -6x+4y=96.
After adding the equations together, you would get -6y=36.
Solving for y, you would find y=-6.
Finally, solving for x, you would substitute the value of y into one of the original equations. Using the first equation, you would get 3x+4(-6)=48. Simplifying, you would get 3x-24=48. Solving for x, you would get x=24/3=8.
Therefore, the solution to the system of equations is x=8 and y=-6.
To solve the given system of equations:
3x + 4y = 48
6x + 2y = 60
1. Choose a method to solve: The best method to solve this system is elimination, as the coefficients of the x variables in both equations are different.
2. Operation to get the x variables to cancel: Multiply the top equation by -2 and the bottom equation by 3 to make the coefficients of x equal and opposite in both equations.
(-2)(3x + 4y) = (-2)(48)
3(6x + 2y) = 3(60)
-6x - 8y = -96
18x + 6y = 180
3. Add the equations together: Line up the equations and add them to get a new equation.
(-6x - 8y) + (18x + 6y) = (-96) + 180
12x - 2y = 84
4. Solve for y: Isolate the y variable in the new equation.
12x - 2y = 84
-2y = -12x + 84
y = (12x - 84) / -2
y = -6x + 42
5. Solve for x: Substitute the value of y back into one of the original equations and solve for x.
3x + 4y = 48
3x + 4(-6x + 42) = 48
3x - 24x + 168 = 48
-21x + 168 = 48
-21x = -120
x = -120 / -21
x = 57.14 (rounded to two decimal places)
6. Find the corresponding values of y: Substitute the value of x back into one of the original equations and solve for y.
3x + 4y = 48
3(57.14) + 4y = 48
171.42 + 4y = 48
4y = 48 - 171.42
4y = -123.42
y = -123.42 / 4
y = -30.8565 (rounded to four decimal places)
Therefore, the solution to the system of equations is x = 57.14 and y = -30.8565.
Note: In the possible solutions you provided, (x=-3, y=18) is not a valid solution for the given system of equations.
To solve the system of equations:
3x + 4y = 48
6x + 2y = 60
We need to determine the best method for solving it by considering how the equations are set up. In this case, the coefficients of x in each equation are not the same, but they have opposite signs. This suggests that the best method to solve the system is elimination.
To cancel out the x variables, we can multiply the bottom equation by 2 and the top equation by -2:
-6x + 4y = -96
12x + 4y = 120
Now, line up the equations together and add them:
-6x + 4y = -96
+ 12x + 4y = 120
________________
+ 6x + 8y = 24
Simplify the top equation by adding the like terms:
6x + 2y = 24
Now, we have a new equation:
6x + 8y = 24
Next, we can solve for y by isolating it in one of the equations. Let's choose the simplified equation:
6x + 2y = 24
Subtract 6x from both sides:
2y = 24 - 6x
Divide both sides by 2:
y = 12 - 3x
Now we have an expression for y.
To solve for x, we can substitute the expression for y into any of the original equations. Let's use the first equation:
3x + 4y = 48
Substitute 12 - 3x in place of y:
3x + 4(12 - 3x) = 48
Expand and simplify:
3x + 48 - 12x = 48
Combine like terms:
-9x + 48 = 48
Subtract 48 from both sides:
-9x = 0
Divide by -9:
x = 0
Now we have the value of x.
Substitute the value of x into the expression for y:
y = 12 - 3(0)
Simplify:
y = 12
So the solution to the system of equations is x = 0 and y = 12.
To summarize, using the method of elimination, we canceled out the x variables by multiplying one equation by -2 and the other equation by 2. We then lined up the equations and added them to obtain a new equation. From there, we solved for y by isolating it in one of the equations and then found the value of x by substituting the expression for y into one of the original equations. Finally, we obtained the solution x = 0 and y = 12.