3x+4y=48
6x+2y=60
1. Choose the best method to solve by looking at the way the equations are set up for you:
graphing, elimination, substitution
2. Using the best method, how could you get the x variables to cancel out? Divide the bottom equation by 2.
Divide the top equation by 4, Multiply the top equation x -2 Multiply the bottom equation x -2.
3. After you complete step 2, what would your top equation be?
x+2y=46, -6x+4y=96, -6x-8y=-96, 3x+y=30
4. Line them up and add the equations together to get: -6=-36, 8y=96, 6y=-96, -8y=-96
5. Solve for y.
6. Solve for x.
To solve the system of equations, we will use the elimination method. We will start by multiplying the top equation by 2 and the bottom equation by 4 to cancel out the x variables.
2*(3x + 4y) = 2*48
6x + 8y = 96
4*(6x + 2y) = 4*60
24x + 8y = 240
Now, we can subtract the second equation from the first equation to eliminate the x variable:
(6x + 8y) - (24x + 8y) = 96 - 240
-18x = -144
x = (-144) / (-18)
x = 8
Next, we substitute the value of x into one of the original equations to solve for y. We will use the first equation:
3x + 4y = 48
3*8 + 4y = 48
24 + 4y = 48
4y = 48 - 24
4y = 24
y = 24 / 4
y = 6
Therefore, the solution to the system of equations is x = 8 and y = 6.
Let's solve the system of equations step-by-step:
1. Since the equations are in standard form, elimination or substitution methods can be used. In this case, let's use the elimination method.
2. To eliminate the x variable, we need to multiply the top equation by 2 and the bottom equation by -3. This will give us:
Top equation: 6x + 8y = 92
Bottom equation: -6x - 6y = -180
3. Now, let's add the modified equations together to eliminate the x variable:
(6x + 8y) + (-6x - 6y) = 92 + (-180)
(6x - 6x) + (8y - 6y) = -88
2y = -88
4. Simplifying further, we have:
2y = -88
5. Now, solve for y by dividing both sides of the equation by 2:
y = -44
6. With the value of y obtained, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
3x + 4(-44) = 48
3x - 176 = 48
3x = 48 + 176
3x = 224
7. Divide both sides of the equation by 3 to solve for x:
x = 224 / 3
Now, you have the solution to the system of equations. The values of x and y are:
x = 224 / 3
y = -44
1. The best method to solve this system of equations is the elimination method. This is because the coefficients of either the x or y variables in both equations are already multiples of each other.
2. To cancel out the x variables, you need to manipulate the equations so that the coefficients of x in both equations are opposites of each other. In this case, you can achieve this by dividing the bottom equation by 2.
3. After dividing the bottom equation by 2 and the top equation by 4, you will have the following equations:
Top equation: x + 2y = 12
Bottom equation: 3x + y = 30
4. To eliminate the x terms, line up the equations and add them together:
(x + 2y) + (3x + y) = 12 + 30
4x + 3y = 42
5. Since the x terms have been eliminated, you can now solve for y by isolating the y variable:
4x + 3y = 42
3y = 42 - 4x
y = (42 - 4x)/3
6. To solve for x, you can substitute the value of y back into one of the original equations:
3x + y = 30
3x + [(42 - 4x)/3] = 30
Multiply both sides of the equation by 3 to get rid of the fraction:
9x + 42 - 4x = 90
Combine like terms:
5x + 42 = 90
Subtract 42 from both sides:
5x = 48
Divide both sides by 5:
x = 9.6
So the solution to the system of equations is x = 9.6 and y = (42 - 4(9.6))/3.