To solve this system you 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 2, using the best method how could
You get the xvariables to cancel out. 3. After you complete step 2 what would
Your top equation be 4. Lime them up and add the equations together to get this equation 5.solve for y 6. Solve for x
1. By looking at the way the equations are set up, the best method to solve this system of equations is by using the elimination method.
2. To get the x variables to cancel out, we can multiply equation 1 by 2 and equation 2 by 3. This will create matching coefficients for the x variable in both equations. The new equations will be:
Equation 1: 6x + 8y = 96
Equation 2: 18x + 6y = 180
3. After completing step 2, the top equation becomes: 6x + 8y = 96.
4. Line up the equations and add them together to get the new equation:
(6x + 8y) + (18x + 6y) = 96 + 180
Simplifying, we get: 24x + 14y = 276
5. Solve for y by isolating the y variable in the new equation:
24x + 14y = 276
Subtract 24x from both sides:
14y = 276 - 24x
Divide both sides by 14:
y = (276 - 24x) / 14
6. Solve for x by substituting the value of y found in step 5 into either equation from the original system. Let's substitute it into equation 1:
3x + 4((276 - 24x) / 14) = 48
Simplifying, we get: 42x + 112 = 4
Subtract 112 from both sides:
42x = -108
Divide both sides by 42:
x = -2.57 (approximately)
Hence, the solution to the system of equations is x = -2.57 and y = (276 - 24x) / 14.
To solve the system of equations:
Step 1: Choose the best method to solve by looking at the way the equations are set up for you. In this case, we have two equations with two variables, so we can use any method: substitution, elimination, or graphing. Let's use the method of elimination.
Step 2: To cancel out the x-variables, we need to multiply both equations by appropriate factors so that the coefficients of x are the same or opposite. In this case, we can multiply the first equation by 2 and the second equation by 3:
(2) * (3x + 4y = 48) ==> 6x + 8y = 96
(3) * (6x + 2y = 60) ==> 18x + 6y = 180
Now we have the same coefficient (6) for x in both equations. The goal is to add or subtract the equations to eliminate the x-variable.
Step 3: After completing step 2, the top equation becomes 6x + 8y = 96.
Step 4: Line up the two equations and add them together to eliminate the x-variable:
(6x + 8y = 96)
+ (18x + 6y = 180)
---------------------------
24x + 14y = 276
Step 5: Now we have a new equation, 24x + 14y = 276, after adding the previous equations together. We can solve this equation for y.
Step 6: Solve for y by isolating the variable. In this case, subtract 24x from both sides of the equation:
24x + 14y = 276
14y = 276 - 24x
y = (276 - 24x) / 14
Step 7: Finally, solve for x by substituting the value of y back into one of the original equations and solving for x.
For example, using the first equation, 3x + 4y = 48, substitute the value of y obtained in step 6:
3x + 4((276 - 24x) / 14) = 48
Now you can simplify and solve for x.
Step-by-step solution:
1. The given system of equations is:
3x + 4y = 48 ...........(Equation 1)
6x + 2y = 60 ...........(Equation 2)
By comparing the coefficients of x in both equations, we can see that 6 is twice the coefficient of x in Equation 1. This suggests that the best method to solve this system is by using the method of elimination.
2. To cancel out the x variables, we multiply Equation 1 by 2 and Equation 2 by -3. This way the coefficients of x in both equations will be equal and opposite:
Multiplying Equation 1 by 2:
2 * (3x + 4y) = 2 * 48
6x + 8y = 96
Multiplying Equation 2 by -3:
-3 * (6x + 2y) = -3 * 60
-18x - 6y = -180
3. After completing step 2, the new top equation becomes:
6x + 8y = 96 ...........(New Equation 1)
4. Now, we line up the equations and add them together:
6x + 8y = 96 ...........(New Equation 1)
-18x - 6y = -180 ...........(Equation 2 multiplied by -1)
Adding both equations:
(6x + 8y) + (-18x - 6y) = 96 + (-180)
-12x + 2y = -84
So, the new equation obtained by adding the equations together is:
-12x + 2y = -84
5. Now, we solve for y by isolating the variable:
-12x + 2y = -84
2y = 12x - 84
y = (12x - 84)/2
y = 6x - 42
6. Finally, to solve for x, we need to substitute the value of y found in step 5 into either of the original equations and solve for x. Let's use Equation 1:
3x + 4y = 48
Substituting y = 6x - 42:
3x + 4(6x - 42) = 48
3x + 24x - 168 = 48
27x - 168 = 48
27x = 48 + 168
27x = 216
x = 216/27
x = 8
So, the solution to the system of equations is x = 8 and y = 6x - 42.