Sure, let's solve the system of equations given by the tuple equality step-by-step.
We start with the equality:
[tex]\[ (x + 2, 4) = (5, y - 2) \][/tex]
From the property of equality of ordered pairs, we know that each corresponding component of the ordered pairs must be equal. Therefore, we can set up two separate equations from this equality:
1. [tex]\( x + 2 = 5 \)[/tex]
2. [tex]\( 4 = y - 2 \)[/tex]
Step 1: Solve for [tex]\( x \)[/tex]
Starting with the first equation:
[tex]\[ x + 2 = 5 \][/tex]
To isolate [tex]\( x \)[/tex], we need to subtract 2 from both sides of the equation:
[tex]\[ x + 2 - 2 = 5 - 2 \][/tex]
[tex]\[ x = 3 \][/tex]
So, the value of [tex]\( x \)[/tex] is:
[tex]\[ x = 3 \][/tex]
Step 2: Solve for [tex]\( y \)[/tex]
Now, let's move to the second equation:
[tex]\[ 4 = y - 2 \][/tex]
To isolate [tex]\( y \)[/tex], we need to add 2 to both sides of the equation:
[tex]\[ 4 + 2 = y - 2 + 2 \][/tex]
[tex]\[ 6 = y \][/tex]
So, the value of [tex]\( y \)[/tex] is:
[tex]\[ y = 6 \][/tex]
Thus, the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy the equation [tex]\( (x + 2, 4) = (5, y - 2) \)[/tex] are:
[tex]\[ x = 3 \][/tex]
[tex]\[ y = 6 \][/tex]
