Solve the system of equations 3x-4y=40 and 5x-5y=55
To solve the system of equations, we'll use the method of substitution.
First, let's solve the second equation for x:
5x - 5y = 55
5x = 55 + 5y
x = (55 + 5y)/5
x = 11 + y
Now we substitute this expression for x into the first equation:
3x - 4y = 40
3(11 + y) - 4y = 40
33 + 3y - 4y = 40
-y = 7
y = -7
Now substitute this value of y back into the expression for x:
x = 11 + y
x = 11 + (-7)
x = 4
Therefore, the solution to the system of equations is x = 4 and y = -7.
To solve the system of equations:
1. We will use the method of substitution. Let's solve one equation for one variable and substitute it into the other equation.
2. Start with the first equation: 3x - 4y = 40.
Solve this equation for x:
3x = 4y + 40
Divide both sides by 3:
x = (4/3)y + (40/3)
Equation (1): x = (4/3)y + (40/3)
3. Now substitute this value of x into the second equation: 5x - 5y = 55.
Replace x with (4/3)y + (40/3) in equation (2):
5((4/3)y + (40/3)) - 5y = 55
Simplify:
(20/3)y + (200/3) - 5y = 55
Multiply both sides by 3 to get rid of the fractions:
20y + 200 - 15y = 165
Combine like terms:
5y + 200 = 165
Subtract 200 from both sides:
5y = -35
Divide both sides by 5:
y = -7
Equation (3): y = -7
4. Now we substitute y = -7 into equation (1) to find x:
x = (4/3)(-7) + (40/3)
Simplify:
x = -28/3 + 40/3
x = 12/3
x = 4
Equation (4): x = 4
5. Therefore, the solution to the system of equations 3x - 4y = 40 and 5x - 5y = 55 is x = 4 and y = -7.
To solve the system of equations 3x - 4y = 40 and 5x - 5y = 55, we can use the method of substitution or elimination. Let's use the method of substitution.
Step 1: Solve one equation for either x or y.
Let's solve the first equation, 3x - 4y = 40, for x:
3x = 4y + 40
Divide both sides of the equation by 3:
x = (4y + 40)/3
Step 2: Substitute the expression found for x into the second equation.
Replace x in the second equation, 5x - 5y = 55, with the expression (4y + 40)/3:
5((4y + 40)/3) - 5y = 55
Step 3: Simplify and solve for y.
Distribute 5 to (4y + 40)/3:
(20y + 200)/3 - 5y = 55
Multiply both sides of the equation by 3 to eliminate the fraction:
20y + 200 - 15y = 165
Combine like terms:
5y + 200 = 165
Subtract 200 from both sides:
5y = -35
Divide both sides by 5:
y = -7
Step 4: Substitute the found value of y back into either of the original equations to solve for x.
Let's substitute y = -7 into the first equation:
3x - 4(-7) = 40
3x + 28 = 40
Subtract 28 from both sides:
3x = 12
Divide both sides by 3:
x = 4
Step 5: Check the solution by substituting the values of x and y into the second equation.
Substituting x = 4 and y = -7 into the second equation 5x - 5y = 55:
5(4) - 5(-7) = 55
20 + 35 = 55
55 = 55
The equation is true, so the solution x = 4 and y = -7 is correct.
Therefore, the solution to the system of equations 3x - 4y = 40 and 5x - 5y = 55 is x = 4 and y = -7.