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KiRa [710]
3 years ago
5

Which property does each equation demonstrate? x2 + 2x = 2x + x2 (3z4 + 2z3) – (2z4 + z3) = z4 + z3 (2x2 + 7x) + (2y2 + 6y) = (2

y2 + 6y) + (2x2 + 7x)
Mathematics
1 answer:
myrzilka [38]3 years ago
5 0

Answer:

1 . Closure

2. Distributive

3. Closure

Step-by-step explanation:

Here, we want to know the type of property exhibited or displayed by each of the equations in the question.

Equation 1 displays the closure property.

What this means that if we make an addition operation either way, we would get same answer. So we say that addition is closed for that equation.

Equation 3 exhibits closure property as well. If we go either way on the addition operation for that equation, we are bound to get the same answer.

Equation 2 exhibits the distributive property.

Each term in the bracket is multiplied by the subtraction symbol before we proceeded to complete the arithmetic operations

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Use elimination to solve.<br> 3y-6x=7<br> -4y-3x=9
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Answer:

x = -5/3, y = -1 or (-\frac{5}{3}, -1)

Step-by-step explanation:

Solving systems of linear equations using process of elimination involves eliminating one of the variables (and its coefficient) in order to solve the other variable either through addition or subtraction. However, there may be other mathematical operations necessary before one of the variables can be eliminated.  

Equation 1:   3y - 6x = 7

Equation 2:  -4y - 3x = 9          

<h3>Step 1:  Multiply Equation 2 by -2:</h3>

(-2)(-4y - 3x) = 9 (-2)

8y + 6x = -18

<h3>Step 2: Add "8y + 6x = -18" to Equation 1:</h3>

  8y + 6x = -18

+ 3y - 6x = 7

11y = -11

<h3>Step 3: Divide both sides by 11 to solve for y:</h3>

\frac{11y}{11} =  \frac{-11}{11}

y = -1

<h3>Step 4: Substitute y = -1 into Equation 2 to solve for x: </h3>

-4(-1) - 3x = 9      

    4 - 3x = 9

<h3>Step 5: Subtract 4 from both sides:</h3>

    4 - 4 - 3x = 9 - 4

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<h3>Step 6: Divide both sides by -3 to solve for x:</h3>

\frac{-3x}{-3} = \frac{5}{-3}

x = - \frac{5}{3}

Verify whether the values for x and y are correct by substituting their values into both equations:

x = -5/3, y = -1

Equation 1:   3y - 6x = 7

3(-1) - 6(-\frac{5}{3}) = 7  

-3 + 10 = 7

7 = 7 (True statement).

Equation 2:  -4y - 3x = 9          

-4(-1) - 3 (-5/3)  = 9          

-4(-1) - 3(-\frac{5}{3}) = 9

4 + 5 = 9

9 = 9  (True statement).

Therefore, x = -5/3 and y = -1 are the solutions to the given systems of linear equations.  

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2 years ago
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