Sure, let's solve the system of equations step-by-step:
Given the system of linear equations:
1. [tex]\( x - y = 5 \)[/tex]
2. [tex]\( x + 2y = -4 \)[/tex]
Step 1: Solve for one variable in terms of the other from one of the equations.
From the first equation [tex]\( x - y = 5 \)[/tex], we can solve for [tex]\( x \)[/tex]:
[tex]\[ x = y + 5 \][/tex]
Step 2: Substitute this expression for [tex]\( x \)[/tex] into the second equation.
Substituting [tex]\( x = y + 5 \)[/tex] into the second equation [tex]\( x + 2y = -4 \)[/tex]:
[tex]\[ (y + 5) + 2y = -4 \][/tex]
Step 3: Simplify and solve for [tex]\( y \)[/tex].
Combining like terms:
[tex]\[ y + 5 + 2y = -4 \][/tex]
[tex]\[ 3y + 5 = -4 \][/tex]
Subtracting 5 from both sides:
[tex]\[ 3y = -4 - 5 \][/tex]
[tex]\[ 3y = -9 \][/tex]
Dividing both sides by 3:
[tex]\[ y = -3 \][/tex]
Step 4: Substitute the value of [tex]\( y \)[/tex] back into the expression for [tex]\( x \)[/tex].
We found that [tex]\( y = -3 \)[/tex]. Using the expression [tex]\( x = y + 5 \)[/tex]:
[tex]\[ x = -3 + 5 \][/tex]
[tex]\[ x = 2 \][/tex]
So, the solution to the system of equations is:
[tex]\[ x = 2 \][/tex]
[tex]\[ y = -3 \][/tex]
Therefore, the solution to the given system of equations is [tex]\( x = 2 \)[/tex] and [tex]\( y = -3 \)[/tex].
