The value of the four integers are; Triangle = 1; Diamond = 5; Square = 2; Clubsuit = 7
We are given the equations;
Triangle + Triangle + Triangle + Triangle + Triangle = Diamond
Triangle + Square + Square = Diamond
Square + Diamond = Clubsuit
If triangle is T, Diamond is D, Square is S and Clubsuit is C, then we have;
5T = D ..... (eq 1)
T + 2S = D .... (eq 2)
S + D = C ......(eq 3)
Equations (1) and (2) are equal. Thus;
5T = T + 2S
4T = 2S
2T = S
T = S/2
Put T + 2S for D in equation (3):
S + T + 2S = C
3S + T = C
3S + S/2 = C
7S/2 = C
Since they are all integers from 1 to 9, it means that T cannot be more than 1 because 5T = D. Thus; T = 1
1 = S/2
S = 2
C = 7 * 2/2
C = 7
D = 5
Read more about Simultaneous equations at; https://brainly.com/question/148035
#SPJ1
