Solve the system.
−5x+4y=48
−5x−8y=24
To solve the system of equations, we can use the method of elimination.
First, we can multiply the second equation by -1 to change the signs:
-5x + 4y = 48
5x + 8y = -24
Now we can add the two equations together to eliminate x:
(-5x + 4y) + (5x + 8y) = 48 + (-24)
12y = 24
y = 2
Now we can substitute this value for y back into one of the original equations to solve for x. Let's use the first equation:
-5x + 4(2) = 48
-5x + 8 = 48
-5x = 40
x = -8
Therefore, the solution to the system of equations is x = -8 and y = 2.
To solve the system of equations:
Equation 1: -5x + 4y = 48
Equation 2: -5x - 8y = 24
We will use the method of elimination to solve the system.
Step 1: Multiply Equation 1 by 2, and Equation 2 by -1 to create a cancelation of 'x' terms:
2 * Equation 1: -10x + 8y = 96
-1 * Equation 2: 5x + 8y = -24
The new system becomes:
Equation 3: -10x + 8y = 96
Equation 4: 5x + 8y = -24
Step 2: Add Equation 3 and Equation 4 together to eliminate the 'x' terms:
(Equation 3) + (Equation 4):
(-10x + 8y) + (5x + 8y) = 96 + (-24)
-10x + 5x + 16y = 72
Simplifying this equation gives us:
-5x + 16y = 72
Step 3: Solve Equation 3 and Equation 4 for 'y' by isolating 'y':
Equation 2 and Equation 4 both give us the value of 'y'. We can choose either equation to solve for 'y'. Let's use Equation 2:
5x + 8y = -24
8y = -5x - 24
y = (-5x - 24) / 8
Step 4: Substitute the value of 'y' in Equation 3 with the equation we obtained in step 3:
-5x + 16((-5x - 24) / 8) = 72
Step 5: Solve for 'x' by simplifying the equation obtained in step 4:
-5x - 20x - 24 = 72
-25x - 24 = 72
-25x = 72 + 24
-25x = 96
x = 96 / -25
x = -3.84
Step 6: Substitute the value of 'x' obtained in step 5 into one of the original equations to solve for 'y'. Let's go back to Equation 1:
-5(-3.84) + 4y = 48
19.2 + 4y = 48
4y = 48 - 19.2
4y = 28.8
y = 28.8 / 4
y = 7.2
So, the solution to the system of equations is x = -3.84 and y = 7.2.
To solve the given system of equations:
Step 1: Method of Elimination
Multiply the second equation by -1 to make the x-coefficients in both equations opposite:
5x + 8y = -24
Step 2: Add the Equations
Add the modified second equation to the first equation:
-5x + 4y + 5x + 8y = 48 - 24
12y = 24
Divide both sides by 12 to solve for y:
y = 2
Step 3: Substitute to Find x
Substitute the value of y = 2 into one of the original equations, let's use the first equation:
-5x + 4(2) = 48
-5x + 8 = 48
Subtract 8 from both sides:
-5x = 48 - 8
-5x = 40
Divide both sides by -5 to solve for x:
x = -8
Step 4: Solution
The solution to the system of equations is x = -8 and y = 2.