To solve this system, you could do the following steps:%0D%0A%0D%0A3x+4y=48%0D%0A3%0D%0A%0D%0A+%0D%0A4%0D%0A%0D%0A=%0D%0A48%0D%0A %0D%0A6x+2y=60%0D%0A6%0D%0A%0D%0A+%0D%0A2%0D%0A%0D%0A=%0D%0A60 To solve this system, you could do the following steps:%0D%0A%0D%0A3x+4y=48%0D%0A3%0D%0A%0D%0A+%0D%0A4%0D%0A%0D%0A=%0D%0A48%0D%0A %0D%0A6x+2y=60%0D%0A6%0D%0A%0D%0A+%0D%0A2%0D%0A%0D%0A=%0D%0A60
To solve this system of equations:
1. Start with the first equation, 3x+4y=48.
2. Multiply the coefficient of x, 3, by the entire second equation, 6x+2y=60. This gives us 18x+6y=180.
3. Multiply the coefficient of y, 4, by the entire second equation, 6x+2y=60. This gives us 24x+8y=240.
4. Subtract the equation from step 2 from the equation from step 3. This gives us 6x+2y=60.
5. Now we have a system of two equations: 6x+2y=60 and 3x+4y=48.
6. Multiply the first equation by -2 to eliminate the y term. This gives us -12x-4y=-120.
7. Add the equation from step 6 to the second equation. This gives us -9x=-72.
8. Solve for x by dividing both sides of the equation by -9. x = 8.
9. Substitute the value of x back into one of the original equations to solve for y. Using the first equation, when x = 8, 3(8) + 4y = 48. This simplifies to 24 + 4y = 48.
10. Subtract 24 from both sides of the equation to isolate the y term. This gives us 4y = 24.
11. Divide both sides of the equation by 4 to solve for y. y = 6.
The solution to the system of equations is x = 8 and y = 6.
To solve the system of equations:
3x + 4y = 48
6x + 2y = 60
We can use the method of substitution or elimination.
Method of Substitution:
Step 1: Solve one equation for one variable. Let's solve the first equation for x:
3x + 4y = 48
3x = 48 - 4y
x = (48 - 4y) / 3
Step 2: Substitute this expression for x into the second equation:
6x + 2y = 60
6((48 - 4y) / 3) + 2y = 60
Simplify:
16y = 60 - 96
16y = -36
y = -36/16 = -9/4
Step 3: Substitute the value of y back into the first equation to find x:
3x + 4(-9/4) = 48
3x - 9 = 48
3x = 48 + 9
3x = 57
x = 57/3 = 19
So the solution to the system of equations is x = 19 and y = -9/4.
Method of Elimination:
Step 1: Multiply the equations by appropriate factors to have the same coefficient for one variable. Let's eliminate the variable x in this case. Multiply the first equation by 2 and the second equation by -1:
2(3x + 4y) = 2(48) => 6x + 8y = 96
-1(6x + 2y) = -1(60) => -6x - 2y = -60
Step 2: Add the two equations together to eliminate the x variable:
(6x + 8y) + (-6x - 2y) = 96 - 60
6y = 36
y = 36/6 = 6
Step 3: Substitute the value of y back into one of the original equations to find x:
3x + 4(6) = 48
3x + 24 = 48
3x = 48 - 24
3x = 24
x = 24/3 = 8
So the solution to the system of equations is x = 8 and y = 6.
Both methods should give the same solution to the system of equations, which is x = 8 and y = 6.
To solve the given system of equations:
1. Start by writing down the two equations:
Equation 1: 3x + 4y = 48
Equation 2: 6x + 2y = 60
2. Pick one equation and solve it for one variable in terms of the other. Let's solve Equation 1 for x:
3x + 4y = 48
Subtract 4y from both sides:
3x = 48 - 4y
Divide both sides by 3:
x = (48 - 4y) / 3
3. Substitute this expression for x in Equation 2:
6x + 2y = 60
Replace x with (48 - 4y) / 3:
6((48 - 4y) / 3) + 2y = 60
4. Simplify the equation:
2(48 - 4y) + 2y = 60
Distribute the 2 to both terms inside the parentheses:
96 - 8y + 2y = 60
Combine like terms:
-6y + 96 = 60
5. Subtract 96 from both sides:
-6y = 60 - 96
-6y = -36
6. Divide both sides by -6:
y = -36 / -6
y = 6
7. Now substitute this value of y back into one of the original equations, let's use Equation 1:
3x + 4(6) = 48
3x + 24 = 48
Subtract 24 from both sides:
3x = 48 - 24
3x = 24
8. Divide both sides by 3:
x = 24 / 3
x = 8
9. The solution to the system of equations is x = 8 and y = 6.