Let 3x + y = 60 and solve the system of equations with 4x + 3y = 120
To solve the system of equations, we can use the method of substitution or elimination.
Method of Substitution:
Step 1: Solve one of the equations for one variable in terms of the other variable.
From the first equation, we can isolate y:
3x + y = 60
y = 60 - 3x
Step 2: Substitute the expression for y in the other equation.
Substituting y = 60 - 3x into the second equation:
4x + 3(60 - 3x) = 120
4x + 180 - 9x = 120
-5x + 180 = 120
-5x = 120 - 180
-5x = -60
x = -60 / -5
x = 12
Step 3: Substitute the value of x back into one of the original equations to find y.
Using the first equation:
3(12) + y = 60
36 + y = 60
y = 60 - 36
y = 24
Therefore, the solution to the system of equations is x = 12 and y = 24.
Method of Elimination:
Step 1: Multiply the first equation by 3 and the second equation by -1 to make the coefficients of y the same.
3(3x + y) = 3(60)
-1(4x + 3y) = -1(120)
9x + 3y = 180
-4x - 3y = -120
Step 2: Add the two resulting equations to eliminate the y term.
(9x + 3y) + (-4x - 3y) = 180 + (-120)
9x - 4x + 3y - 3y = 60
5x = 60
x = 60 / 5
x = 12
Step 3: Substitute the value of x back into one of the original equations to find y.
Using the first equation:
3(12) + y = 60
36 + y = 60
y = 60 - 36
y = 24
Therefore, the solution to the system of equations is x = 12 and y = 24.
To solve the system of equations:
1. 3x + y = 60
2. 4x + 3y = 120
We can use the method of elimination to eliminate one variable and solve for the other. Here's how:
Step 1: Multiply equation 1 by 3 to match the coefficients of 'y' in both equations:
(3 * 3x) + (3 * y) = (3 * 60)
9x + 3y = 180
Step 2: Now we have the equations:
9x + 3y = 180 (equation 3)
4x + 3y = 120 (equation 2)
Step 3: Subtract equation 2 from equation 3 to eliminate 'y':
(9x + 3y) - (4x + 3y) = 180 - 120
(9x - 4x) + (3y - 3y) = 60
5x + 0 = 60
5x = 60
x = 60 / 5
x = 12
Step 4: Substitute the value of x into any of the original equations (e.g., equation 1) to solve for 'y':
3x + y = 60
3 * 12 + y = 60
36 + y = 60
y = 60 - 36
y = 24
Step 5: So, the solution to the system of equations is x = 12 and y = 24.