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

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.

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 ✓

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

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.

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

3(-1) + 8(4) = 29
 - 3 + 32 = 29
 29 = 29 prove
 
Therefore (-1,4) is a solution for 3x + 8y = 29..

3(-1)+8(4)=29=>
the answer is "correct".

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.

3x  + 8y   = 29
3 (- 1 )   + 8 (4)   = - 3  + 32   =  29
Thus (-1,4) is a solution

3(-1)+8(4)=29.  -3+32=29.
Yes.

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

Yes, its that simple!

3 x  +  8 y  =   29

If ( - 1, 4 ) satisfy the equation --

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

Hence Point ( - 1, 4 )  is  a solution to the given equation. .............. Answer