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.
Answer:
(1.5,-2.6)
Step-by-step explanation:
Given the polar coordinates (-3,60°).
Let our Cartesian coordinates be (x,y)
#We know that when converting the rectangular coordinates (x,y) to polar (r,θ), then:
#Using the illustration above, we can express our polar coordinates as:
#Solve simultaneously to solve for x and y:
Hence, the Cartesian coordinates are (1.5,-2.6)