The 2 equations are classified as Identities because both sides remain the same for all values of z.
1) We are given the equation;
23z + 19 = 3(5z - 9) + 8z + 46
Let us try z = 0
23(0) + 19 = 3(5(0) - 9) + 8(0) + 46
19 = -27 + 46
19 = 19
Let us try z = 5;
23(5) + 19 = 3(5(5) - 9) + 8(5) + 46
134 = 48 + 40 + 46
134 = 134
Thus, this is an identity as both sides remaining the same for all values of z.
2) We are given the equation;
15y + 32 = 2(10y - 7) - 5y + 46
At y = 0, we have;
15(0) + 32 = 2(10(0) - 7) - 5(0) + 46
32 = -14 + 46
32 = 32
Let us try y = 2;
15(2) + 32 = 2(10(2) - 7) - 5(2) + 46
62 = 26 - 10 + 46
62 = 62
This is an identity as both sides remaining the same for all values of z.
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