o 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
To solve the system of equations, we can use the method of substitution or elimination. I will use the 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 the expression for x into the second equation.
6x + 2y = 60
6((48-4y)/3) + 2y = 60
Simplify:
16y/3 + 2y = 60
Step 3: Solve for y.
Multiplying the equation by 3 to get rid of the fraction:
16y + 6y = 180
22y = 180
y = 180/22
y = 90/11
Step 4: Substitute the value of y back into one of the equations to solve for x.
x = (48 - 4(90/11))/3
x = (48 - 360/11)/3
x = (528/11 - 360/11)/3
x = 168/11 / 3
x = 168/33
x = 56/11
Therefore, the solution to the system of equations is:
x = 56/11
y = 90/11
To solve this system of equations:
Equation 1: 3x + 4y = 48
Equation 2: 6x + 2y = 60
Step 1: Choose a method of solving the system. In this example, we will use the method of elimination.
Step 2: Multiply Equation 2 by -2 to make the coefficients of y in both equations the same.
-2 * (6x + 2y) = -2 * 60
-12x - 4y = -120
The new equation is: -12x - 4y = -120
Step 3: Add the modified Equation 2 to Equation 1.
3x + 4y = 48
+ (-12x - 4y = -120)
________________________
-9x = -72
Step 4: Solve for x by dividing both sides of the equation by -9.
-9x / -9 = -72 / -9
x = 8
Step 5: Substitute the value of x (x = 8) into one of the original equations, such as Equation 1, to solve for y.
3(8) + 4y = 48
24 + 4y = 48
Step 6: Simplify the equation by subtracting 24 from both sides.
4y = 48 - 24
4y = 24
Step 7: Solve for y by dividing both sides of the equation by 4.
4y / 4 = 24 / 4
y = 6
Step 8: The solution to the system of equations is x = 8 and y = 6.
Therefore, the solution to the system is x = 8 and y = 6.
To solve the given system of equations, you can use the method of substitution or the method of elimination. Here, I will explain how to solve it using the method of substitution.
Step 1: Start with the first equation of the system:
3x + 4y = 48
Step 2: Solve the first equation for one variable in terms of the other variable. Let's solve it for x:
3x = 48 - 4y
Divide both sides by 3:
x = (48 - 4y) / 3
Step 3: Substitute this value of x into the second equation of the system:
6x + 2y = 60
Substitute the value of x we found in step 2:
6((48 - 4y) / 3) + 2y = 60
Step 4: Simplify the equation:
Expand and simplify the expression, and get rid of the denominator by multiplying every term by 3:
2(48 - 4y) + 6(2y) = 60
96 - 8y + 12y = 60
Combine like terms:
4y + 96 = 60
Subtract 96 from both sides:
4y = 60 - 96
4y = -36
Divide both sides by 4:
y = -9
Step 5: Substitute the value of y back into either equation to find the value of x. Let's use the first equation:
3x + 4y = 48
Substitute y = -9:
3x + 4(-9) = 48
3x - 36 = 48
Add 36 to both sides:
3x = 48 + 36
3x = 84
Divide both sides by 3:
x = 84 / 3
x = 28
Step 6: Verify the solution by substituting the values of x and y back into both equations:
Checking the first equation:
3x + 4y = 48
3(28) + 4(-9) = 48
84 - 36 = 48
48 = 48 (true)
Checking the second equation:
6x + 2y = 60
6(28) + 2(-9) = 60
168 - 18 = 60
150 = 60 (false)
The solution x = 28 and y = -9 only satisfies the first equation. Therefore, there is no solution for the given system of equations.