How do you solve the following system of equations?: #x-2y=13 , x - y= 10#?

Question

Eva Abramson · Accepted Answer

lettuce solve for #x# as it is same in both equations #1^(st)equation#
#x-2y=13#
Transfer #2y#
#x=13+2y# #2^(nd)equation#
#x-y=10#
Put value of #x#
#13+2y-y=10#
Solve
#13+y=10#
Transfer #13#
#y=10-13#
#color(red)(y=-3#
#x=13+2y#
#x=13+2xx-3#
#x=13-6#
#color(red)(x=7#

Hazel Anglin · Answer

undefined To solve the system of equations $x - 2y = 13$ and $x - y = 10$, you can use the method of substitution or elimination. Here's how you can solve it using the substitution method:

1. Solve one of the equations for one variable in terms of the other.
   Let's solve $x - y = 10$ for $x$: $x = y + 10$.

2. Substitute the expression found in step 1 into the other equation.
   Substitute $x = y + 10$ into $x - 2y = 13$: $(y + 10) - 2y = 13$.

3. Solve the resulting equation for the variable.
   Expand and simplify: $y + 10 - 2y = 13$ becomes $10 - y = 13$.
   Rearrange and solve for $y$: $10 - 13 = y$ implies $y = -3$.

4. Once you have found the value of one variable, substitute it back into one of the original equations to solve for the other variable.
   Substitute $y = -3$ into $x - y = 10$: $x - (-3) = 10$.
   Simplify: $x + 3 = 10$.
   Solve for $x$: $x = 7$.

So, the solution to the system of equations is $x = 7$ and $y = -3$.