Given the equation y − 4 = 2 ( x + 1 ) y-4=2\left(x+1\right) , which of the following ordered pairs is a solution?

this problem, we are given the equation y minus four equals two times x plus one. Which of the following ordered pairs is a solution based off the ordered pairs we have? Okay. So let's go through this. Now the main way to check to see if an ordered pair is a solution is to plug in your points for x and y, and to see if the statement that you have is true. Now I'm gonna go ahead and start this by checking a. Now to check 'a', what that means is we have this point negative one negative four, and recall points are always in this form of x and y. So I just need to plug these into the equation above, and that's going to tell me whether that is a true statement. So notice here that y is negative four and x is one. So going up to this equation, we're going to replace y with negative four. So we have negative four minus four, and we want to see if this is going to equal two times negative one, since negative one is our x, plus one. So let's see what happens if we go through this math. Well, we're going to have negative four minus four, which comes out to negative eight, and we wanna check if this is equal to two times negative one plus one which comes out to zero. So we end up getting the negative eight equals zero, and obviously this is not a true statement. Negative eight does not equal zero. So because we got that this is not equivalent, we would say that point a is not a solution. We're trying to figure out which of these is a solution, and clearly a is not the correct answer. But now let's check b. For b we have the point zero six. So to check this I'm going to replace my y's with six and my x's with zero. So going up here we're going to have zero minus four is equal to two times, and then in this case, or actually no this is y, so that should be a six right there. So we're going to have six minus four, but you got to be careful with that because it's easy to accidentally mix up the points, but so my y here is going to be six, then we're going to have that that's two times x plus one, which is gonna be zero plus one. So notice how I've replaced x with zero and y with six, six minus four is two, and then two times zero plus one, well that's gonna give me two times one. We wanna see if these are equal to each other, and two times one is two, so we get a two equals two, this is a true statement. So because of that we can say that option b is going to be a solution, this ordered pair will be a solution to the given equation. Now we already found our answer, but just to make sure we know this, I'm gonna check c and d as well. Let's go ahead and check c. For c, we have the point one four, so that's going to have our y value of four plugged in, and we'll have that minus four is equal to two times x plus one. And so that's going to give us x, which is one, and then we're gonna have plus one. So we wanna see if these are equal. Four minus four is zero, and then we're going to have two times one plus one, which is two times two over four. Clearly, zero does not equal four. So because of that, we can say that this zero equals four, this is not true either, so c does not check out. But now we can finally check d, which is our last case here. So let's check the point two seven. So what I'm going to do is take my y here and replace it with seven. Well, seven minus four is equal to two times and then this is a two here, replacing with x, so two plus one. In this case, we have seven minus four, which comes out to three. And then we have two times two plus one, which is three. We're seeing if these are equal, and two times three is six, clearly three does not equal six, so d does not work either. Now we it's important to check all these points here because it's possible we could have had multiple points that were a solution. I mentioned before that we got this point, but notice that this problem says which of the following ordered pairs is a solution. So in this case, we saw that it was b, but it's important to check over all points just to make sure that there are any other cases that would work as well, because there could possibly be multiple solutions, and it's just good to understand this process for checking if a point is a solution. So I hope you found this video helpful, and let's move on and get some more practice. See you in the next one.

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Multiple Choice

Given the equation $y - 4 = 2 (x + 1)$ , which of the following ordered pairs is a solution?

$(- 1, - 4)$

$open paren 0 comma 6 close paren$

$open paren 1 comma 4 close paren$

$open paren 2 comma 7 close paren$

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Verified step by step guidance

Start with the given equation: $y - 4 = 2\left(x + 1\right)$.

To check if an ordered pair $(x, y)$ is a solution, substitute the $x$-value and $y$-value from the pair into the equation.

For example, if you want to test the pair $(0, 6)$, substitute $x = 0$ and $y = 6$ into the equation to get: $6 - 4 = 2\left(0 + 1\right)$.

Simplify both sides: calculate $6 - 4$ on the left and $2 \times (0 + 1)$ on the right.

If both sides are equal after substitution and simplification, then the ordered pair is a solution to the equation.

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Struggling with Beginning & Intermediate Algebra?

Given the equation y−4=2(x+1)y-4=2\(\left\)(x+1\(\right\)), which of the following ordered pairs is a solution?

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Given the equation $y - 4 = 2 (x + 1)$ , which of the following ordered pairs is a solution?