Question

circle = type your answer...
sun = type your answer...
square = type your answer...
triangle = type your answer...

Explanation:

Step1: Let circle be $c$, sun be $s$, square be $q$, triangle be $t$.

From the first - row: $c + s + s+q=18$, which simplifies to $c + 2s+q = 18$.
From the second - row: $c + q + s+q=20$, which simplifies to $c + s+2q = 20$.
From the third - row: $t + t + c+t=10$, which simplifies to $c + 3t = 10$.
From the fourth - row: $q + t + q+s=14$, which simplifies to $s + 2q+t = 14$.

Step2: From $c + 3t = 10$, we can express $c = 10 - 3t$.

Substitute $c = 10 - 3t$ into $c + 2s+q = 18$: $10 - 3t+2s+q = 18$, so $2s+q=8 + 3t$.
Substitute $c = 10 - 3t$ into $c + s+2q = 20$: $10 - 3t+s+2q = 20$, so $s + 2q=10 + 3t$.

Step3: Multiply the equation $s + 2q=10 + 3t$ by 2: $2s + 4q=20 + 6t$.

Subtract $2s+q=8 + 3t$ from $2s + 4q=20 + 6t$:
$(2s + 4q)-(2s+q)=(20 + 6t)-(8 + 3t)$.
$3q = 12 + 3t$, so $q = 4 + t$.

Step4: Substitute $q = 4 + t$ into $s + 2q=10 + 3t$:

$s+2(4 + t)=10 + 3t$.
$s + 8+2t=10 + 3t$, so $s=t + 2$.

Step5: Substitute $s=t + 2$ and $q = 4 + t$ into $s + 2q+t = 14$:

$(t + 2)+2(4 + t)+t = 14$.
$t + 2+8 + 2t+t = 14$.
$4t+10 = 14$.
$4t = 4$, so $t = 1$.

Step6: Since $t = 1$:

$q = 4 + t=5$.
$s=t + 2=3$.
$c = 10 - 3t=7$.

Answer:

Circle = 7
Sun = 3
Square = 5
Triangle = 1