Let's call the prices of citrons and apples [tex] c [/tex] and [tex] a [/tex], respectively.
The first equation means
[tex] 8c+7a=37 [/tex]
While the second translates to
[tex] 7c+8a = 38 [/tex]
Multiply the first equation by [tex] 7 [/tex], and the second by [tex] 8 [/tex] to get
[tex] \left \{ {{56c+49a=259} \atop {56c+64a=304}} \right. [/tex]
Now subtract the first equation from the second to get
[tex] 15a = 45 \iff a=3 [/tex]
plus this value in the first equation (for example) to get
[tex] 8c+7\cdot 3 = 37 \iff 8c+21=37 \iff 8c = 16 \iff c=2 [/tex]
So, the cost of a citron is [tex] 2 [/tex]
