5x - 4y = -44
- x + 3y = 22
To solve the given system of equations, we can use the method of substitution or elimination.
We'll use the method of elimination:
First, let's multiply the second equation by 5 to make the coefficients of x in both equations the same:
- x + 3y = 22
Multiplying both sides by 5:
-5x + 15y = 110
Now, we can add the two equations:
5x - 4y = -44
-5x + 15y = 110
Adding the two equations together:
(-5x + 5x) + (-4y + 15y) = -44 + 110
0x + 11y = 66
11y = 66
Now, we can solve for y by dividing both sides by 11:
11y/11 = 66/11
y = 6
Now, substitute the value of y back into one of the original equations to solve for x:
- x + 3(6) = 22
- x + 18 = 22
- x = 22 - 18
- x = 4
Therefore, the solution to the given system of equations is x = 4 and y = 6.
To solve this system of equations:
Step 1: Choose one of the equations and isolate one variable in terms of the other variable. Let's solve the second equation for x:
- x + 3y = 22
Add x to both sides:
3y = x + 22
Substitute this into the first equation:
5(x + 22) - 4y = -44
Step 2: Distribute and simplify the first equation:
5x + 110 - 4y = -44
Step 3: Combine like terms:
5x - 4y = -44 - 110
5x - 4y = -154
Step 4: Now we have a new system of equations:
5x - 4y = -154
- x + 3y = 22
Step 5: Multiply the second equation by 5 to eliminate x:
5(- x + 3y) = 5(22)
- 5x + 15y = 110
Step 6: Now we have the following system of equations:
5x - 4y = -154
- 5x + 15y = 110
Step 7: Add the two equations together to eliminate x:
(5x - 4y) + (- 5x + 15y) = (-154) + 110
- 4y + 15y = - 44
11y = - 44
Step 8: Solve for y:
y = - 44 / 11
y = - 4
Step 9: Substitute the value of y back into one of the original equations (let's use the second equation):
- x + 3(-4) = 22
- x - 12 = 22
- x = 22 + 12
- x = 34
Step 10: The solution to the system of equations is x = 34 and y = -4.