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Leni [432]
3 years ago
9

6+8x-9=11x+14-3x, can this equation be always, sometimes, or never true.

Mathematics
1 answer:
goblinko [34]3 years ago
4 0
To answer the question above, simplify both sides of the equation. This gives,
                         8x - 3 = 8x + 14
Next, cancel the term 8x because it appears on both sides of the equation giving,
                             -3 = 14
That is NOT true. Therefore, the answer is the equation is NEVER TRUE.
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fiasKO [112]

Answer:

A. Solutions are: x = 2, y = 1.

B. Solutions are: x = 3, y = 2.

C.

1. Inconsistent

2. Inconsistent

3. Consistent

Step-by-step explanation:

A. Solutions of each system of linear equations by substitution method:

Equation 1:      3x - 2y = 4

Equation 2:               x = 2y

<u>Step 1:</u> Substitute x = 2y into the Equation 1:

3(2y) - 2y = 4

6y - 2y = 4

4y = 4

Step 2: Divide both sides of the equation by 4 to isolate y:

\frac{4y}{4}  = \frac{4}{4}

y = 1.

<u>Step 3:</u> For Equation 2, x = 2y, substitute y = 1 into the equation to solve for x:

x = 2y  

x = 2(1)

x = 2  

Therefore, the solutions are:  x = 2, y = 1.

B. Find the solutions of each system of linear equations by elimination method:  

Equation 1:      2x + y = 8

Equation 2:        x + y = 5

<u>Step 1:</u> Multiply Equation 2 by 2:  

2(x + y) =  5(2)

2x + 2y = 10

<u>Step 2:</u> Subtract Equation 1 from the equation derived from Step 1,  2x + 2y = 10:

   2x + 2y = 10

-  <u>2x +  y  =   8</u>

        y =   2

Step 3: Plug in y =  2 into Equation 1, 2x + y = 8 to solve for x:

2x + y = 8

2x + (2) = 8

<u>Step 4:</u> subtract both sides of the equation by 2 to isolate x:

2x + 2 - 2 = 8 - 2

2x = 6

<u>Step 5:</u> Divide both sides of the equation by 2 to solve for x:

\frac{2x}{2}  = \frac{6}{2}

x = 3.

The solutions are: x = 3, y = 2.

C:

1. Inconsistent

2. Inconsistent  

3. Consistent (infinitely many solutions)

3 0
3 years ago
What's the solution of the following linear system?<br><br> y = 4x + 1<br><br> y = 4x
allochka39001 [22]
The solution of a system of equations is the point at which the two lines intersect. Since y is already isolated, we can set the equations equal to each other by doing:
4x=4x+1
Subtract 4x from both sides
0=1
Since 0 cannot equal 1 in any case, the lines never intersect. There is no solution to the problem.
7 0
3 years ago
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