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 possible solutions for this system of equations are:
- substitution: y = -12, x = 6
- graphing: y = 18, x = -3
- elimination: y = -12, x = 6
The operation to get the x variables to cancel is to multiply the bottom equation by 2.
The simplified top equation after step 2 would be -6x + 4y = 96.
To solve the given system of equations:
3x + 4y = 48 ...(Equation 1)
6x + 2y = 60 ...(Equation 2)
The best method to solve this system is by using the elimination method.
To get the x variables to cancel out, we need to multiply Equation 1 by -2 and Equation 2 by 3:
-6x - 8y = -96 ...(Equation 1 multiplied by -2)
18x + 6y = 180 ...(Equation 2 multiplied by 3)
When we add these two equations together, the x variables will cancel out:
(-6x - 8y) + (18x + 6y) = -96 + 180
12y = 84
y = 7
Now, we can substitute the value of y back into one of the original equations to solve for x. Let's use Equation 1:
3x + 4(7) = 48
3x + 28 = 48
3x = 48 - 28
3x = 20
x = 20/3
So the solution to the system of equations is x = 20/3 and y = 7.
Using the elimination method, the x variables canceled out by adding the equations:
-6x - 8y + 18x + 6y = -96 + 180
12y - 2y = 84
10y = 84
y = 8.4
Now, substitute the value of y back into Equation 1:
3x + 4(8.4) = 48
3x + 33.6 = 48
3x = 48 - 33.6
3x = 14.4
x = 14.4/3
So the solution to the system of equations is x ≈ 4.8 and y ≈ 8.4.
To solve the system of equations:
3x + 4y = 48
6x + 2y = 60
We will use the elimination method to get the x variables to cancel out.
To do this, we can choose to multiply the bottom equation by 2 to make the coefficients of the x term the same. This way, when we add the equations together, the x terms will cancel out.
2 * (6x + 2y) = 2 * 60
12x + 4y = 120
Now line up the equations and add them:
3x + 4y = 48
12x + 4y = 120
This yields the equation:
15x = 168
Now solve for x:
x = 168 / 15
x = 11.2
Now substitute this value back into either equation to solve for y. Let's choose the first equation:
3(11.2) + 4y = 48
33.6 + 4y = 48
4y = 48 - 33.6
4y = 14.4
y = 14.4 / 4
y = 3.6
So the solution to the system of equations is x = 11.2 and y = 3.6.
Alternatively, you can solve this system using the substitution or graphing method.