Solve the system of equations. 3x−4y=40 5x−5y=55
To solve this system of equations using the elimination method, we can multiply the first equation by 5 and the second equation by 3 to make the coefficients of x in both equations the same:
5 * (3x - 4y) = 5 * 40
3 * (5x - 5y) = 3 * 55
Which simplifies to:
15x - 20y = 200
15x - 15y = 165
Now, we can subtract the second equation from the first equation to eliminate x:
(15x - 20y) - (15x - 15y) = 200 - 165
This simplifies to:
-20y + 15y = 35
Combining like terms:
-5y = 35
Dividing both sides by -5:
y = -7
Now, we substitute this value back into one of the original equations to solve for x. Let's use the first equation:
3x - 4(-7) = 40
3x + 28 = 40
Subtracting 28 from both sides:
3x = 12
Dividing both sides by 3:
x = 4
Therefore, the solution to the system of equations is x = 4 and y = -7.
To solve the system of equations:
Equation 1: 3x - 4y = 40
Equation 2: 5x - 5y = 55
There are several methods to solve the system, such as substitution, elimination, or graphing. Let's use the elimination method:
Step 1: Multiply Equation 1 by 5 and Equation 2 by 3 to make the x coefficients the same:
Multiply Equation 1 by 5: 15x - 20y = 200
Multiply Equation 2 by 3: 15x - 15y = 165
Step 2: Subtract Equation 2 from Equation 1 to eliminate the x terms:
(15x - 20y) - (15x - 15y) = 200 - 165
15x - 20y - 15x + 15y = 35
-20y + 15y = 35
-5y = 35
y = 35 / -5
y = -7
Step 3: Substitute the value of y back into one of the original equations to solve for x:
Using Equation 1: 3x - 4(-7) = 40
3x + 28 = 40
3x = 40 - 28
3x = 12
x = 12 / 3
x = 4
Therefore, the solution to the system of equations is x = 4 and y = -7.
To solve the system of equations:
3x - 4y = 40
5x - 5y = 55
You can use either the substitution method or the elimination method to find the values of x and y that satisfy both equations.
Let's use the elimination method:
Multiply the first equation by 5 and the second equation by 3 to make the coefficients of x in both equations the same:
(5)(3x - 4y) = (5)(40)
(3)(5x - 5y) = (3)(55)
This simplifies to:
15x - 20y = 200
15x - 15y = 165
Now subtract the second equation from the first equation:
(15x - 20y) - (15x - 15y) = 200 - 165
This simplifies to:
-20y + 15y = 35
Combine like terms:
-5y = 35
Divide both sides of the equation by -5 to solve for y:
y = 35 / -5
Simplifying:
y = -7
Now substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:
3x - 4(-7) = 40
Simplifying:
3x + 28 = 40
Subtract 28 from both sides:
3x = 40 - 28
This simplifies to:
3x = 12
Divide both sides of the equation by 3 to solve for x:
x = 12 / 3
Simplifying:
x = 4
Therefore, the solution to the system of equations is x = 4 and y = -7.