2x - y = 5 5x + y = 16
2 answers:
Answer:
(3, 1)
Step-by-step explanation:
To find the solution (point of intersection) of a system of linear equations, first convert them to <u>slope-intercept form</u> (y=mx+b) by isolating "y". Then, equate their expressions to find "x". Substitute what you find for "x" to find the coordinate for "y".
<u>Isolate "y" in each equation</u>
Subtract 2x from both sides
Divide the whole equation by -1 to isolate "y"
Each term's negative/positive sign changes
Subtract 5x from both sides
The 5x on left cancel out (5x - 5x = 0)
Since y = 2x - 5 and y = -5x + 16 both equal y, we can make them equal each other. Then isolate "x" to be on the left side.
<u>Equate the equations</u>
y = y
2x - 5 = -5x + 16
2x - 5 + 5x = -5x + 5x + 16 Add 5x to both sides
2x - 5 + 5x = 16 Right side 5x cancelled out (-5x + 5x = 0)
7x - 5 = 16 Combined like terms on left (2x + 5x = 7x)
7x - 5 + 5 = 16 + 5 Add 5 to both sides.
7x = 16 + 5 Left side cancelled out (-5 + 5 = 0)
7x = 21 Simplified right side.
7x/7 = 21/7 Divide both sides by 7
x = 21/7 Since 7/7=1, 7x/7 = x , and "x" is isolated.
x = 3 Found "x" coordinate of solution.
<u>Substitute x = 3</u> into any equation
2x - y = 5
2(3) - y = 5 Simplify first by multiplying 2 and 3 on left side
6 - y = 5 Start isolating "x"
6 - y + y = 5 + y Add "y" to both sides.
6 = 5 + y Left side y's cancelled out (-y + y = 0)
6 - 5 = 5 - 5 + y Subtract 5 from both sides
6 - 5 = y Right side cancelled out (5 - 5 = 0)
1 = y Answer after left side simplified (6 - 5=1)
y = 1 Standard formatting puts variable on left
<u>Write the solution as an ordered pair</u> in the form (x, y).
The solution to the linear system is (3, 1).
<u>Check</u> if this is correct by <u>substituting x=3 and y=1</u> into both equations:
2x - y = 5
2(3) - 1 = 5 Simplify 2 times 3
6 - 1 = 5 Subtract
5 = 5 Same answer
LS = RS Left side equals right side
Correct
5x + y = 16
5(3) + 1 = 16 Simplify 5 times 3
15 + 1 = 16 Add
16 = 16 Same answer
LS = RS Left side equals right side
Correct.
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Given:
You spin the spinner once.
The possibilities are 6, 8, 17.
To find:
The probability of getting a prime number, i.e., P(prime).
Solution:
In the given numbers 6, 8, 17, only 17 is a prime number because it is divisible by 1 and itself.
6 and 8 are divisible by 2, so they are not prime.
The probability (in %) of getting a prime number is:
Therefore, the correct option is A.