Explain or show that the point (5, -4) is a solution to this system of equations: 3x - 2y = 23

2x + y = 6

Using the concept of simultaneous equation, the solution to the system of equations is (5, - 4)

Given the system of linear equations :

From (2) :

Substitute (3) into (1)

3x - 2(6 - 2x) = 23

3x - 12 + 4x = 23

7x = 23 + 12

7x = 35

Divide both sides by 7 to isolate x

x = 35 / 7

x = 5

From (3)

y = 6 - 2(5)

y = 6 - 10

y = -4

Therefore, the solution to the system of equation is (5, - 4)

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Step-by-step explanation:

If (5, - 4) is a solution to the system then both equations will be true when (5, - 4) is substituted into them.

Substitute (5, - 4) into the left side of the equations and if equal to the right side then (5, - 4) is a solution.

3(5) - 2(- 4) = 15 + 8 = 23 = right side

2(5) + (- 4) = 10 - 4 = 6 = right side

Then (5, - 4) is a solution to the system of equations.

or by solving

3x - 2y = 23 → (1)

2x + y = 6 → (2)

Multiplying (2) by 2 and adding to (1) will eliminate the y- term

4x + 2y = 12 → (3)

Add (1) and (3) term by term to eliminate y, that is

7x = 35 ( divide both sides by 7 )

x = 5

Substitute x = 5 into either of the 2 equations and solve for y

Substituting into (2)

2(5) + y = 6

10 + y = 6 ( subtract 10 from both sides )

y = - 4

Solution is (5, - 4 )

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step-by-step explanation:

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560