Consider this system of linear equations:
22x − y = -23 (equation 1)
11x + 12y = 1 (equation 2)
ok. now what?
I know. Why not write them as
22x − y = -23
22x + 24y = 2
guess what comes next?
To solve this system of linear equations, you can use the method of elimination or substitution. I will explain how to solve it using the method of elimination.
Step 1: Multiply equation 1 by 12 and equation 2 by -1 (this will create opposites for the y-term):
Equation 1 becomes: 264x - 12y = -276 (equation 3)
Equation 2 becomes: -11x - 12y = -1 (equation 4)
Step 2: Add equation 3 and equation 4 together:
(264x - 12y) + (-11x - 12y) = -276 + (-1)
264x - 12y - 11x - 12y = -277
253x - 24y = -277 (equation 5)
Step 3: Simplify equation 5:
253x - 24y = -277
Step 4: Solve equation 5 for x:
253x = -277 + 24y
x = (-277 + 24y)/253 (equation 6)
Step 5: Substitute the value of x from equation 6 into equation 1 to solve for y:
22((-277 + 24y)/253) - y = -23
(-6094 + 528y)/253 - y = -23
Step 6: Solve the equation above for y:
-6094 + 528y - 253y = -23 * 253
-6094 + 528y - 253y = -58619
275y = -52525
y = -52525/275
y = -191
Step 7: Substitute the value of y = -191 into equation 6 to solve for x:
x = (-277 + 24(-191))/253
x = (-277 - 4584)/253
x = -4861/253
Therefore, the solution to the system of linear equations is x = -4861/253 and y = -191.