To solve this system, you could do the following steps:
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: 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.
To solve the system of equations:
1. The best method to solve can be determined by analyzing the equations. In this case, since both equations have coefficients that can be easily cancelled out by manipulating the equations, the elimination method would be the best approach.
2. To cancel out the x variables, we can multiply the first equation by 2 and the second equation by 3:
Equation 1: 2(3x + 4y) = 2(48) which simplifies to 6x + 8y = 96
Equation 2: 3(6x + 2y) = 3(60) which simplifies to 18x + 6y = 180
3. After completing step 2, the top equation would be: 6x + 8y = 96
4. Line up the equations together and add them:
(6x + 8y) + (18x + 6y) = 96 + 180
This simplifies to 24x + 14y = 276
5. Solve for y:
24x + 14y = 276
Rearrange the equation: 14y = 276 - 24x
Divide both sides by 14: y = (276 - 24x) / 14
6. Solve for x:
Substitute the value of y from step 5 into one of the original equations, such as Equation 1:
3x + 4y = 48
3x + 4((276 - 24x) / 14) = 48
Multiply both sides by 14 to remove the fraction: 42x + 4(276 - 24x) = 672
Expand and simplify: 42x + 1104 - 96x = 672
Combine like terms: -54x + 1104 = 672
Subtract 1104 from both sides: -54x = -432
Divide both sides by -54: x = 8
Now that we have x=8, substitute this value back into one of the original equations to find the value of y:
3(8) + 4y = 48
24 + 4y = 48
Subtract 24 from both sides: 4y = 24
Divide both sides by 4: y = 6
Therefore, the solution to the system of equations is x = 8 and y = 6.
1. The best method to solve this system of equations is by elimination.
2. To get the x variables to cancel out, we need to multiply the first equation by 2 and the second equation by 3. This will make the coefficients of the x variables the same in both equations, allowing us to eliminate them when we add the equations together.
3. After completing step 2, the top equation would be:
6x + 8y = 96
4. Line up the equations and add them together:
(6x + 8y) + (6x + 2y) = 96 + 60
12x + 10y = 156
5. Solve for y by isolating it on one side of the equation:
12x + 10y = 156
10y = 156 - 12x
y = (156 - 12x)/10
y = 15.6 - 1.2x
6. To solve for x, substitute the expression for y back into one of the original equations:
3x + 4(15.6 - 1.2x) = 48
3x + 62.4 - 4.8x = 48
-1.8x + 62.4 = 48
-1.8x = 48 - 62.4
-1.8x = -14.4
x = -14.4 / -1.8
x = 8
Therefore, the solution to the system of equations is x = 8 and y = 15.6 - 1.2(8) = 4.8.
1. To choose the best method to solve this system of equations, we need to look at the coefficients of the variables. In this case, the coefficients of x in the two equations are 3 and 6, and the coefficients of y are 4 and 2. Since the coefficients of x are multiples of each other and the coefficients of y are not multiples of each other, let's use the method of elimination.
2. To get the x variables to cancel out, we need to multiply the equations by suitable constants such that the coefficients of x in both equations become negatives of each other or equal. In this case, we can multiply the first equation by 2 and the second equation by 3 to make the coefficients of x in both equations equal to -6.
3. After completing step 2, the top equation would be:
6x + 8y = 96 (since 2 * (3x + 4y) = 2 * 48)
4. Now, let's line up the equations and add them together to get a new equation:
(6x + 8y) + (6x + 2y) = 96 + 60
12x + 10y = 156
5. To solve for y, we can isolate the y term on one side of the equation. Subtract 12x from both sides of the equation:
12x + 10y - 12x = 156 - 12x
10y = 156 - 12x
6. Finally, solve for x by isolating the x term on one side of the equation. Divide both sides of the equation by 10:
10y/10 = (156 - 12x)/10
y = (156 - 12x)/10
Now, we have the equations y = (156 - 12x)/10 and 6x + 2y = 60. You can substitute the value of y in the second equation from step 6 and solve for x. Once you have the value of x, you can substitute it back into the first equation from step 6 and solve for y.