Solve the following system of equations. Express your answer as an ordered pair in format (a,b), with no spaces between the numb
ers or symbols. 3x+4y=16 and -4x-3y=-19
2 answers:
Remark
There are two ways to do this. You can graph the equations (which I have included at the end of the question using Desmos) or you can solve it algebraically which in this case is going to be slightly painful.
Algebra
Multiply the first equation by 4 and the second by 3
<em><u>First Equation</u></em>
4 [3x + 4y = 16]
12x + 16y = 64 (3)
<em><u>Second Equation</u></em>
3 [-4x - 3y = - 19]
- 12x - 9y = - 57 (4)
Add (3) and (4)
12x + 16y = 64
<u>- 12x - 9y = -57 </u> Add
7y = 7 Divide by 7
y = 1
Solve for x
3x + 4y = 16 Let y = 1
3x + 4(1) = 16
3x + 4 = 16 Subtract 4
3x = 12 Divide by 3
x = 12/3
x = 4
Answer
(4,1) just as the graph suggests.
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Hey there,
Let's remember that a (inequality symbol) is things like (<), (>), (≤),(≥), (≠).
So, I believe that (-3x+7) and (-10-2) are separate. So we will find that out :)
Let's first do (-3x+7). As simplifying this expression here, we take that "x" of for a while and just stick to (-3+7).
-3
+ 7
______
4
Let's bring that "x" back, and the answer would be 4x for a while.
So far, 4x is the answer.
_____________________________________________________________
Now, Let's work on the other side.
We are talking about (<span>-10-2)
-10
- 2
_______
</span> -12
So, by solving the answer to (-10-2), we got -12.
So, let's determine what is greater . . . . .
-12 or 4.
-12 is on the negative side, and the number 4 is positive. This would conclude that 4 is great than -12.
Your correct answer would look like . . .
<span>(-3x+7) > (-10-2)
</span>
I really hope this helps you alot.
~Jurgen
Let's remember that a (inequality symbol) is things like (<), (>), (≤),(≥), (≠).
So, I believe that (-3x+7) and (-10-2) are separate. So we will find that out :)
Let's first do (-3x+7). As simplifying this expression here, we take that "x" of for a while and just stick to (-3+7).
-3
+ 7
______
4
Let's bring that "x" back, and the answer would be 4x for a while.
So far, 4x is the answer.
_____________________________________________________________
Now, Let's work on the other side.
We are talking about (<span>-10-2)
-10
- 2
_______
</span> -12
So, by solving the answer to (-10-2), we got -12.
So, let's determine what is greater . . . . .
-12 or 4.
-12 is on the negative side, and the number 4 is positive. This would conclude that 4 is great than -12.
Your correct answer would look like . . .
<span>(-3x+7) > (-10-2)
</span>
I really hope this helps you alot.
~Jurgen