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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The complete question is as follows.
The equation a = can be used to determine the area , <em>a</em>, of a trapezoid with height , h, and base lengths,
and
. Which are equivalent equations?
(a)
(b)
(c) =
(d)
(e) = h
Answer: (a) ; (d)
;
Step-by-step explanation: To determine :
a =
2a = ()h
To determine h:
a =
2a =
= h
To determine
a =
2a =
Checking the alternatives, you have that and
= h, so alternatives <u>A</u> and <u>D</u> are correct.