How do you solve the following system of equations?: #x+y= -2 , x-2y=13#?

Question

Savannah Anderson · Accepted Answer

#x = 3#
#y = -5# You add/subtract the two equations with each other, using the #=# sign as a point of reference: #x+y = -2# would be the first equation. We can label it as equation #(1)# #x-2y = 13# would be the second equation. We can label it as equation #(2)# Now, we can subtract equation #(2)# from equation #(1)# [the idea here is to leave us with only one variable, that way we can solve the equation as usual] #(1) - (2)# would be #x-x + y-(-2y) = -2-13# #0 + 3y = -15# so #y = -5# Now we can take #y# and use it in equation #(1)#; #x+(-5) = -2# #x = 3# So #x = 3 and y = -5#

Ethan Adkins · Answer

#x = 3#
#y = -5# since we have two unknowns we need minimum of two equations to solve for them , and we have that too lets see the first equation #x+y =-2# the first objective is to write either x in terms of y or y in terms of x so i add -y to both sides , and we get #x = -2-y# take this value of x and plug it in equation 2 so this #x-2y=13# becomes #(-2-y)-2y =13# solve for y to get a value #-2 -3y = 13 # #-3y = 15# #-y = 5# or # y = -5# since we got y value , we can plug it back in the first equation to get x value #x + (-5) = -2# or #x = 5-2 = 3# So , #x=3 , y=-5#

Kennedy Adams · Answer

undefined To solve the system of equations:

1. Choose one of the equations and solve for one variable in terms of the other variable.
2. Substitute the expression obtained in step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Once you find the value of one variable, substitute it back into one of the original equations to find the value of the other variable.
5. Verify the solution by substituting both values into the other equation to ensure it holds true.

Given the system:
x + y = -2
x - 2y = 13

From the first equation, solve for x:
x = -2 - y

Substitute x = -2 - y into the second equation:
(-2 - y) - 2y = 13

Solve for y:
-2 - y - 2y = 13
-2 - 3y = 13
-3y = 15
y = -5

Substitute y = -5 into the first equation to find x:
x + (-5) = -2
x - 5 = -2
x = -2 + 5
x = 3

Therefore, the solution to the system is x = 3 and y = -5.