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:
On a coordinate plane, a line has a negative slope
Step-by-step explanation:
A linear function is a function whose graph is a straight line. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function.
Answer:
a) -$3.03; b) The $5 on the number 25
Step-by-step explanation:
To find the expected value, multiply each probability by its value and then add them together.
The probability of making a profit of $20 is 3/38; this gives us
3/38(20) = 60/38
The probability of losing $5 is 35/38; this gives us
35/38(-5) = -175/38
Together, this gives us
60/38-175/38 = -115/38 ≈ $-3.03
b) Since the expected value for the $5 bet on a single number is $-0.53, and the expected value for the $5 on either 00, 0 or 1 is $-3.03, the better bet is on the number 25. The expected value loses less money with this option.
