Question

Is (5,50) a solution to the linear system y = 5x + 25 and y = 3x + 35? Explain your reasoning.

Answer 1

Answer:  Yes (5, 50) is a solution

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Explanation:

The point (5, 50) means x = 5 and y = 50 pair up together.

Plug those values into the first equation and simplify both sides as much as possible. This is so we have one number on each side.

y = 5x+25

50 = 5*5+25

50 = 25+25

50 = 50

Because we ended up with a true statement at the end, this makes the original equation y = 5x+25 to be true when (x,y) = (5,50).

In other words, the first equation has been confirmed.

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Repeat those steps for the second equation

y = 3x+35

50 = 3*5+35

50 = 15+35

50 = 50

We get another true statement, and we've confirmed the second equation.

Both equations are true when (x,y) = (5, 50)

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This fully confirms that (5, 50) is indeed a solution to this system.

It turns out it's the only solution. Visually we can verify this by looking at the graph. The two lines intersect at one location and it is (5, 50).

See below.