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.
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.
1 answer
1 answer