How do you solve by substitution #x-y+-15# and #x+y=-5#?

Question

Eva Adamson · Accepted Answer

Assuming the first component should have (#=-#) instead of (#+-#) [1]#color(white)("XXXX")##x-y = -15#
[2]#color(white)("XXXX")##x+y=-5# Rearranging the terms of [1]
[3]#color(white)("XXXX")##x= y-15# Substituting #(y-15)# for #x# into [2]
[4]#color(white)("XXXX")##(y-15) + y = -5#
[5]#color(white)("XXXX")##y=5# Substituting #5# for #y# back in [1]
[6]#color(white)("XXXX")##x - 5 = -15#
[7]#color(white)("XXXX")##x = -10# Solution: #(x,y) = (-10,5)#

Eva Adamson · Answer

undefined To solve the system of equations by substitution:

1. Solve one of the equations for one variable in terms of the other variable.
2. Substitute this expression into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Once you have found the value of one variable, substitute it back into one of the original equations to find the value of the other variable.

Given the equations x - y = -15 and x + y = -5:

1. From the second equation, solve for x:
   x = -5 - y.

2. Substitute this expression for x into the first equation:
   -5 - y - y = -15.

3. Simplify and solve for y:
   -5 - 2y = -15.
   -2y = -15 + 5.
   -2y = -10.
   y = -10 / -2.
   y = 5.

4. Now that we have found the value of y, substitute it back into one of the original equations to find x. Using the second equation:
   x + 5 = -5.
   x = -5 - 5.
   x = -10.

So, the solution to the system of equations is x = -10 and y = 5.

Genesis Allen · Answer

undefined To solve the system of equations $x - y = -15$ and $x + y = -5$ by substitution, we can isolate one of the variables in one equation and substitute it into the other equation.

First, isolate $x$ in the second equation:
$$x + y = -5$$
$$x = -5 - y$$

Now substitute $x = -5 - y$ into the first equation:
$$-5 - y - y = -15$$
$$-5 - 2y = -15$$

Add 5 to both sides:
$$-2y = -10$$

Divide both sides by -2:
$$y = 5$$

Now substitute $y = 5$ into $x = -5 - y$:
$$x = -5 - 5$$
$$x = -10$$

So, the solution to the system of equations is $x = -10$ and $y = 5$.