# To determine whether (−1,4) is a solution to the equation 3x+8y=29, substitute blank for x and blank for y.?

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• When you are given an "ordered pair" as a position, the order will always be (x, y)

(unless the question explicitly tells you otherwise - it is very rare)

Therefore, the ordered pair (-1, 4) means x = -1 and y = +4

If the point is a solution, then the values will "satisfy" the equation - meaning that the equation will be true if you put in these values.

3x + 8y = 29

becomes

3(-1) + 8(4) = -3 + 32 = 29

the equation is "true" when we use the values, therefore the ordered pair is a solution.

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• The pair of numbers in parentheses is (x,y).

It means x is -1 at the same time that y is 4.

Substitute -1 for x and 4 for y

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• 3(-1) + 8(4) = 29

- 3 + 32 = 29

29 = 29 prove

Therefore (-1,4) is a solution for 3x + 8y = 29..

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• For the equation, 3x + 8y = 29,

determine whether (−1, 4) is a solution.

Yes one solution is indeed (−1, 4).

There is the possibility of other solutions.

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• 3x  + 8y   = 29

3 (- 1 )   + 8 (4)   = - 3  + 32   =  29

Thus (-1,4) is a solution

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• 3(-1)+8(4)=29.  -3+32=29.

Yes.

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• In general, if you have an equation and an (x,y) pair to test as a solution, you simply plug in the values and see if the equation is a true statement.

In your example, to check if (-1,4) is a solution to the equation 3x + 8y = 29, you plug in -1 for x and 4 for y.

Let's do that:

3(-1) + 8(4) =? 29

-3 + 32 =? 29

29 = 29 ✓

By substituting in -1 for x and 4 for y, you can show that (-1,4) *is* a solution to that equation.

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• 3x + 8y = 29

3x = 29 - 8y

x = (29 - 8y)/3 → then you substitute y by its given value, i.e.: 4

x = (29 - 32)/3

x = - 3/3

x = - 1 ← you can see that it's the given value for x

You can conclude that (- 1 ; 4) is a solution.

…and to go further, you can say that the point (- 1 ; 4) belongs to the line: 3x + 8y = 29

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• Yes, its that simple!

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• For the equation 3x + 8y = 29

When x = -1 and y = 4:

L.H.S. = 3(-1) + 8(4) = -3 + 32 = 29 = R.H.S.

Hence, (-1, 4) is a solution to the equation 3x + 8y = 29.

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