Certainly! Let's solve the shape equation puzzle step by step.
We are given two equations:
1. [tex]\( + = 14 \)[/tex]
2. [tex]\( - = 2 \)[/tex]
Let's use variables to make it easier to solve. Assume:
- [tex]\( + = x \)[/tex]
- [tex]\( - = y \)[/tex]
Then we can rewrite the equations as:
1. [tex]\( x + y = 14 \)[/tex]
2. [tex]\( x - y = 2 \)[/tex]
First, we'll add these two equations together to eliminate [tex]\( y \)[/tex]:
[tex]\[
(x + y) + (x - y) = 14 + 2
\][/tex]
Simplifying this, we get:
[tex]\[
2x = 16
\][/tex]
Now, solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{16}{2}
\][/tex]
[tex]\[
x = 8
\][/tex]
With [tex]\( x = 8 \)[/tex], we can substitute this value back into one of the original equations to find [tex]\( y \)[/tex]. Let's use the first equation:
[tex]\[
8 + y = 14
\][/tex]
Subtract 8 from both sides to solve for [tex]\( y \)[/tex]:
[tex]\[
y = 14 - 8
\][/tex]
[tex]\[
y = 6
\][/tex]
Therefore, the values that solve the shape equation puzzle are:
[tex]\[
+ = 8
\][/tex]
[tex]\[
- = 6
\][/tex]
So we have [tex]\( x = 8 \)[/tex] and [tex]\( y = 6 \)[/tex].
