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Schach [20]
3 years ago
12

I need help 6x-2y=10 x-2y=-5 solve by elimination

Mathematics
1 answer:
dem82 [27]3 years ago
8 0
<h3><u>Explanation</u></h3>
  • Given the system of equations.

\begin{cases} 6x - 2y = 10 \\ x - 2y =  - 5 \end{cases}

  • Solve the system of equations by eliminating either x-term or y-term. We will eliminate the y-term as it is faster to solve the equation.

To eliminate the y-term, we have to multiply the negative in either the first or second equation so we can get rid of the y-term. I will multiply negative in the second equation.

\begin{cases} 6x - 2y = 10 \\  - x  +  2y =  5 \end{cases}

There as we can get rid of the y-term by adding both equations.

(6x - x) + ( - 2y + 2y) = 10 + 5 \\ 5x + 0 = 15 \\ 5x = 15 \\ x =  \frac{15}{5}  \longrightarrow  \frac{ \cancel{15}}{ \cancel{5}}  =  \frac{3}{1}  \\ x = 3

Hence, the value of x is 3. But we are not finished yet because we need to find the value of y as well. Therefore, we substitute the value of x in any given equations. I will substitute the value of x in the second equation.

x - 2y =  - 5 \\ 3 - 2y =  - 5 \\ 3 + 5 = 2y \\ 8 = 2y \\  \frac{8}{2}  = y \\ y =  \frac{8}{2} \longrightarrow  \frac{ \cancel{8}}{ \cancel{2}}  =  \frac{4}{1}  \\ y = 4

Hence, the value of y is 4. Therefore, we can say that when x = 3, y = 4.

  • Answer Check by substituting both x and y values in both equations.

<u>First</u><u> </u><u>Equation</u>

6x - 2y = 10 \\ 6(3) - 2(4) = 10 \\ 18 - 8 = 10 \\ 10  = 10 \longrightarrow \sf{true} \:  \green{ \checkmark}

<u>Second</u><u> </u><u>Equation</u>

x - 2y =  - 5 \\ 3 - 2(4) =  - 5 \\ 3 - 8 =  - 5 \\  - 5 =  - 5 \longrightarrow  \sf{true} \:  \green{ \checkmark}

Hence, both equations are true for x = 3 and y = 4. Therefore, the solution is (3,4)

<h3><u>Answer</u></h3>

\begin{cases} x = 3 \\ y = 4 \end{cases} \\  \sf \underline{Coordinate \:  \: Form} \\ (3,4)

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3 years ago
Write the equation in slope-intercept form then change it to standard form with integer coefficients.
SCORPION-xisa [38]

Answer:

1. Slope-intercept form:   y = 2x - 4

Standard form:   2x - y = 4

2. Slope-intercept form:  y = \dfrac12x - 1

Standard form:             x - 2y = 2

3. Slope-intercept form:   y = \dfrac45x + \dfrac{21}{5}

Standard form:            4x -5y = - 21

Step-by-step explanation:

Slope intercept form:   y = mx + b

where:

  • y = y-coordinate
  • m = slope
  • x = x-coordinate
  • b = y-intercept

Standard form:  Ax + By = C

\textsf{1.  as} \ m=2: \ \ y = 2x + b

   \textsf{at} \  (6, 8): \ \ 8 = 2(6) + b

   \implies b = -4

Slope-intercept form:   y = 2x - 4

Standard form:   2x - y = 4

\textsf{2.  as} \  \ m = \dfrac12: \ \ y = \dfrac12x + b

    \textsf{at} \  (4, 1): \ \ 1 = \dfrac12(4) + b

    \implies b = -1

Slope-intercept form:  y = \dfrac12x - 1

Standard form:             x - 2y = 2

\textsf{3.  as} \  \ m = \dfrac45: \ \ y = \dfrac45x + b

   \textsf{at} \  (1,5): \ \ 5 = \dfrac45(1) + b

   \implies b = \dfrac{21}{5}

Slope-intercept form:   y = \dfrac45x + \dfrac{21}{5}

Standard form:            4x -5y = - 21

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Step-by-step explanation:

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3 years ago
Zohar is using scissors to cut a rectangle with a length of 5x - 2 and a width of 3x + 1 out of a larger piece of paper. Which
kirza4 [7]

Answer:

2*(5x - 2) + 2*(3x+1) ; Perimeter = 62 centimeters

Step-by-step explanation:

2*(5x - 2) + 2*(3x+1) = 10x - 4 + 6x + 2

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If x = 4 , then Perimeter = 16*4 - 2 = 64 - 2 = 62 cm

4 0
3 years ago
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How much smaller is the sum of the first 1000 natural numbers than the sum of the first 1001 natural numbers?
aleksandr82 [10.1K]

ANSWER

1001

EXPLANATION

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The sum of the first 1000 terms is

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S_{1000}=500 (1001)

S_{1000}=500500

The sum of the first 1001 terms is

S_{1001}=  \frac{1001}{2} (2(1) + 1(1001 - 1))

S_{1001}= 1001 \times (501)

= 501501

The difference is

501501 - 500500= 1001

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3 years ago
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