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Given: 32 = 2x + 4y; x = 2

Prove: y=7

substitution property:
substraction property of equality:
division property of equality:
symmetric property of equality

fill in the blanks

32 = 2x + 4y

32 = 2(2) + 4y
32 = 4 + 4y
28 = 4y
7 = y

Did you know?

In algebra, several properties are used to prove mathematical equations. One such property is the substitution property, which allows us to replace a variable with its value in an equation. Another property is the subtraction property of equality, which states that when the same value is subtracted from both sides of an equation, the equality is preserved. The third property is the division property of equality, which states that when both sides of an equation are divided by the same nonzero value, the equality is maintained. Lastly, we have the symmetric property of equality, where if two expressions are equal, then switching the order of the expressions does not affect the equality. These properties can be utilized to solve equations, such as the given equation 32 = 2x + 4y, where x = 2. By leveraging these properties, we can prove that y = 7.