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.
One possible method to solve this system of equations is to use the method of substitution.
To cancel out the x variables, we can multiply the first equation by 2 and the second equation by -3:
2(3x+4y) = 2(48)
-3(6x+2y) = -3(60)
This gives us:
6x + 8y = 96
-18x - 6y = -180
Now, we can line up the equations and add them together:
(6x + 8y) + (-18x - 6y) = 96 + (-180)
Simplifying this equation gives us:
-12x + 2y = -84
We can solve for y by isolating it on one side of the equation:
2y = -84 + 12x
y = -42 + 6x
Now that we have the equation for y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
3x + 4(-42 + 6x) = 48
Simplifying this equation gives us:
3x - 168 + 24x = 48
27x - 168 = 48
27x = 216
x = 8
Now that we have the value of x, we can substitute it back into the equation for y:
y = -42 + 6(8)
y = -42 + 48
y = 6
Therefore, the solution to the system of equations is x = 8 and y = 6.
To solve the given system of equations:
1. The best method to solve this system is by using the method of elimination, as the coefficients of the x variables in both equations are already multiples of each other (3 and 6).
2. To make the x variables cancel out, we can multiply the first equation by -2 and the second equation by 4:
Equation 1: -2(3x + 4y) = -2(48) => -6x - 8y = -96
Equation 2: 4(6x + 2y) = 4(60) => 24x + 8y = 240
3. Line up the equations and add them together:
-6x - 8y + 24x + 8y = -96 + 240
=> 18x = 144
=> x = 8
4. Now that we have obtained the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:
3x + 4y = 48
=> 3(8) + 4y = 48
=> 24 + 4y = 48
=> 4y = 48 - 24
=> 4y = 24
=> y = 6
Therefore, the solution to the system of equations is x = 8 and y = 6.
To solve the given system of equations:
1. Look at the coefficients of the x variables in both equations. In this case, the coefficients are 3 and 6. Since 3 can go into 6 evenly, we can use the method of elimination to cancel out the x variables by multiplying one or both equations by a suitable factor.
2. In this case, we can multiply the first equation by 2 and the second equation by -1, which will result in the coefficients of the x variables being -6 and 6, allowing them to cancel out when added together.
Multiply the first equation by 2:
2(3x + 4y) = 2(48)
6x + 8y = 96
Multiply the second equation by -1:
-1(6x + 2y) = -1(60)
-6x - 2y = -60
3. Line up the two modified equations and add them together to eliminate the x variables:
(6x + 8y) + (-6x - 2y) = 96 + (-60)
6x - 6x + 8y - 2y = 96 - 60
6y = 36
4. Solve for y by dividing both sides of the equation by 6:
6y/6 = 36/6
y = 6
5. Substitute the found value of y (y = 6) back into one of the original equations to solve for x. Let's use the first equation:
3x + 4(6) = 48
3x + 24 = 48
6. Solve for x by isolating the x variable:
3x = 48 - 24
3x = 24
7. Divide both sides of the equation by 3 to find the value of x:
3x/3 = 24/3
x = 8
So, the solution to the given system of equations is x = 8 and y = 6.