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 x variables to cancel out?
3. After you complete step 2, what would your top equation be?
4. Line them up and add the equations together to get:
5. Solve for y.
6. Solve for x.
1. The best method to solve this system of equations is the method of elimination.
2. To get the x variables to cancel out, we can multiply the first equation by 2 and the second equation by -3.
3. After multiplying the equations, we would have:
6x + 8y = 96
-18x - 6y = -180
4. Line them up and add the equations together to get:
-12y = -84
5. Solving for y, we divide both sides of the equation by -12:
y = 7
6. Substituting the value of y back into one of the original equations, we can solve for x:
3x + 4(7) = 48
3x + 28 = 48
3x = 48 - 28
3x = 20
x = 20/3 or 6.67
1. The best method to solve this system of equations is to use the method of substitution since one of the equations can be easily rearranged to solve for one variable in terms of the other.
2. To get the x variables to cancel out, we can rearrange one of the equations to solve for one variable in terms of the other, and then substitute that expression into the other equation.
3. Let's solve the second equation, 6x + 2y = 60, for x:
Subtract 2y from both sides:
6x = 60 - 2y
Divide both sides by 6:
x = (60 - 2y) / 6
Now we have x in terms of y.
4. Substituting the expression for x into the first equation, 3x + 4y = 48:
Replace x with (60 - 2y) / 6:
3((60 - 2y) / 6) + 4y = 48
Simplify the expression:
(60 - 2y) / 2 + 4y = 48
Multiply both sides by 2 to eliminate the fraction:
(60 - 2y) + 8y = 96
Simplify further:
60 - 2y + 8y = 96
Combine like terms:
6y + 60 = 96
5. Now, we can solve for y by isolating the y variable:
Subtract 60 from both sides:
6y = 96 - 60
Simplify:
6y = 36
Divide both sides by 6:
y = 36 / 6
y = 6
6. To find the value of x, substitute the value of y into either of the original equations, let's use the first equation:
3x + 4(6) = 48
Simplify:
3x + 24 = 48
Subtract 24 from both sides:
3x = 48 - 24
3x = 24
Divide both sides by 3:
x = 24 / 3
x = 8
So the solution to the system of equations is x = 8 and y = 6.
1. The best method to solve this system of equations is to use the method of elimination.
2. To cancel out the x variables, we can multiply the second equation by 2 and the first equation by 6, so that the coefficients of the x terms will be the same in both equations.
3. After performing the multiplication, the top equation becomes 18x + 24y = 288.
4. Line them up and add the equations together to get:
(18x + 24y) + (6x + 2y) = 288 + 60
This simplifies to:
24x + 26y = 348.
5. Solve for y by isolating the variable:
24x + 26y = 348
26y = 348 - 24x
y = (348 - 24x)/26
6. Solve for x by substituting the value of y into one of the original equations. Let's use the first equation:
3x + 4y = 48
3x + 4((348 - 24x)/26) = 48
Multiply both sides by 26 to eliminate the fraction:
78x + 4(348 - 24x) = 1248
Simplify and solve for x:
78x + 1392 - 96x = 1248
-18x + 1392 = 1248
-18x = 1248 - 1392
-18x = -144
x = -144/-18
x = 8.
Thus, the solution to the system of equations is x = 8 and y = (348 - 24(8))/26, which can be further simplified.