Final answer:
Using the multiplication property of equality, one can multiply or divide both sides of an algebraic equation by the same number to find the value of an unknown variable. In an equation like 3y = 6, dividing both sides by 3 gives the solution y = 2. This concept is applicable to solving all linear equations.
Step-by-step explanation:
Understanding Algebraic Equations
When working with algebraic equations, it's important to understand the properties of equality. For example, multiplication property of equality allows us to multiply both sides of an equation by the same nonzero number without changing the equality of the equation. This is useful for solving equations and finding the value of an unknown variable.
Let's consider the algebraic equation 3y = 6. To solve for y, we divide both sides by 3, which is using the multiplication property of equality in reverse (in this case, it's the division property of equality). Division is just multiplication by the reciprocal. So when we divide both sides by 3, we are actually multiplying both sides by 1/3. This gives us y = 2, which is an equivalent equation because the balance of the equation is maintained.
Linear equations such as 7y = 6x + 8, 4y = 8, and y + 7 = 3x follow the same principles. When we manipulate these equations by using properties of equality, we do not change the relationship between variables. Hence, when graphing linear equations like y = 9 + 3x, all the points that satisfy the equation form a straight line on the graph, representing the solution set of that equation.