You want to eliminate one of the terms (x or y) in one of the equations so you can solve for the other variable. You have to multiply by the opposite number of the coefficient to be able to eliminate the term in the other equation. If the x coefficient is 2, then you have to multiply the entire other equation by -2. If the y coefficient is -5, then you have to multiply the entire other equation by 5.
10)
-4x + 9y= 9
x - 3y= -6
STEP 1:
multiply the bottom equation by 4
4(x- 3y)= 4(-6)
4x - 12y= -24
STEP 2:
add the top equation and the equation from step 2
-4x + 9y= 9
4x - 12y= -24
the x term cancels out
-3y= 15
divide both sides by -3
y= -5
STEP 2:
substitute the y value in either original equation to solve for x
x - 3y= -6
x - 3(-5)= -6
x + 15= -6
subtract 15 from both sides
x= -21
ANSWER: x= -21; y= -5
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12)
-7x + y= -19
-2x + 3y= -19
STEP 1:
multiply the top equation by -3 to eliminate the y term and to solve for x
-3(-7x + y)= -3(-19)
21x - 3y= 57
STEP 2:
add the bottom equation and the equation from step 2 to solve for x
-2x + 3y= -19
21x - 3y= 57
the y term cancels out
19x= 38
divide both sides by 19
x= 2
STEP 3:
substitute the x value in step 2 to solve for y; you can use either original equation
-7x + y= -19
-7(2) + y= -19
-14 + y= -19
add 14 to both sides
y= -5
ANSWER: x= 2; y=-5
Hope this helps! :)
Answer:
a couple of irrational numbers: -16±4√19, approximately {1.436, -33.436}
Step-by-step explanation:
Your question can be cast as the quadratic equation
x² +32x -48 = 0
The solutions can be found using the quadratic formula:
x = (-32 ±√(32² -4(1)(-48)))/(2(1)) = -16±√304 = -16±4√19
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<em>Comment on the equation we used</em>
We notice that when p and q are roots, the equation can be written ...
(x -p)(x -q) = 0 = x² -(p+q)x +pq
You want p+q = -32, pq = -48, so the equation is ...
x² -(-32)x +(-48) = 0
x² +32x -48 = 0 . . . . . . with parentheses eliminated
Answer:
correct
Step-by-step explanation:
Imagine a point in the top left quadrant of a graph
when you rotate it 180 degrees it will end up in the bottom right quadrant
The same will apply if you flip on the y axis and the x axis in no given order
Answer:
-20x+27
Step-by-step explanation:
-4(5x-3)+15 Distribute First
-20x+12+15 Simplify
-20x+27 All Done!
