Question

problem 1
solve this system of equations:
$2x + y = 10$
$x + y = 6$
use the shape puzzle if it helps with your thinking

variable	value?
$y$	5

(and a shape puzzle with two stars and a house = 10, one star and a house = 6)

Explanation:

Step1: Subtract the second equation from the first

We have the system:

$$\begin{cases} 2x + y = 10 \\ x + y = 6 \end{cases}$$

Subtract the second equation from the first: $(2x + y) - (x + y) = 10 - 6$.
Simplify: $2x + y - x - y = 4$, so $x = 4$.

Step2: Substitute x = 4 into the second equation

Substitute $x = 4$ into $x + y = 6$: $4 + y = 6$.
Solve for y: $y = 6 - 4 = 2$.

Answer:

The solution is $x = 4$ and $y = 2$.