To solve the system of equations, we can use the method of elimination or substitution.
Method 1: Elimination
1. Multiply both sides of the second equation by 4 to eliminate the y term:
4(5x - 5y) = 4(55)
20x - 20y = 220
2. Multiply both sides of the first equation by 5 to eliminate the y term:
5(3x - 4y) = 5(40)
15x - 20y = 200
3. Subtract the new second equation from the new first equation:
(20x - 20y) - (15x - 20y) = 220 - 200
20x - 15x - 20y + 20y = 20
5x = 20
x = 4
4. Substitute the value of x into one of the original equations, such as the first equation:
3x - 4y = 40
3(4) - 4y = 40
12 - 4y = 40
-4y = 40 - 12
-4y = 28
y = -7
5. The solution to the system of equations is x = 4 and y = -7.
Method 2: Substitution
1. Solve one of the equations for one variable in terms of the other variable. Let's solve the first equation for x:
3x - 4y = 40
3x = 40 + 4y
x = (40 + 4y)/3
2. Substitute this expression for x into the second equation:
5x - 5y = 55
5((40 + 4y)/3) - 5y = 55
(200 + 20y)/3 - 5y = 55
(200 + 20y) - 15y = 165
200 + 20y - 15y = 165
5y = -35
y = -7
3. Substitute the value of y into the expression for x:
x = (40 + 4(-7))/3
x = (40 - 28)/3
x = 12/3
x = 4
4. The solution to the system of equations is x = 4 and y = -7.
Both methods yield the same solution: x = 4 and y = -7.
Solve the system of equations
3x-4y=40
5x-5y=55
1 answer