If the equation $y=8-3x$ is substituted into the equation $9x+2y=500$, which of these is the resulting equation?

Substitute y = 8 − 3 x into 9 x + 2 y = 500 .
Distribute and simplify: 9 x + 2 ( 8 − 3 x ) = 500 becomes 9 x + 16 − 6 x = 500 .
Combine like terms: 3 x + 16 = 500 .
The resulting equation is 3 x + 16 = 500 ​ .

Explanation

Understanding the Problem We are given two equations:

y = 8 − 3 x and 9 x + 2 y = 500 .
We need to substitute the first equation into the second equation to find the resulting equation.

Substitution Substitute y = 8 − 3 x into the equation 9 x + 2 y = 500 . This means we replace y in the second equation with the expression 8 − 3 x from the first equation.

Substituting the expression This gives us:


9 x + 2 ( 8 − 3 x ) = 500

Distributing Now, we simplify the equation by distributing the 2:

9 x + 16 − 6 x = 500

Combining Like Terms Next, we combine like terms (the terms with x ):

( 9 x − 6 x ) + 16 = 500
3 x + 16 = 500

Final Equation So, the resulting equation is:

3 x + 16 = 500
Examples
Substitution is a powerful tool used in various real-life scenarios. For instance, imagine you're baking a cake and need to adjust the recipe for a different number of servings. If the original recipe calls for a certain amount of flour based on the number of eggs, and you decide to use a different number of eggs, you would substitute the new egg quantity into the flour equation to find the adjusted amount of flour needed. This ensures your cake turns out perfectly, even with recipe adjustments. Similarly, in physics, if you know the velocity of an object as a function of time, you can substitute that expression into the equation for distance to find the distance traveled as a function of time.

Answered by GinnyAnswer | 2025-07-07

After substituting y = 8 − 3 x into 9 x + 2 y = 500 , the resulting equation is 3 x + 16 = 500 .
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Answered by Anonymous | 2025-07-12