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Nostrana [21]
3 years ago
5

−5x + y = −2 −3x + 6y = −12 solved by substitution please work so i can understand

Mathematics
2 answers:
Arte-miy333 [17]3 years ago
7 0

Answer:

x=0 and y= -2

Step-by-step explanation:

−5x+y=−2for y:

−5x+y=−2

−5x+y+5x=−2+5x(Add 5x to both sides)

y=5x−2

5x−2foryin−3x+6y=−12:

−3x+6y=−12

−3x+6(5x−2)=−12

27x−12=−12(Simplify both sides of the equation)

27x−12+12=−12+12(Add 12 to both sides)

27x=0

x=0

Substitute0 for X in y=5x−2:

y=5x−2

y=(5)(0)−2

y=−2(Simplify both sides of the equation)

Lunna [17]3 years ago
5 0
Make y subject:
y = -2 + 5x
Sub into other equation as y:
-3x + 6(-2 + 5x) = -12
-3x -12 + 30x = -12
27x = 0
x = 0
Sub in X to find Y:
-5(0) + y = -2
y = -2
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Using the quadratic formula to solve 5x = 6x2 – 3, what are the values of x?
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<span>6x2 -5x –3 = 0
a = 6 b=-5 and c=-3

x = [-b +-sq root (b² -4ac)] / 2a
x = [--5 +-sq root (25 -4*6*-3)] / 2*6
x = [5 +- sq root (25 +72)] / 12
x = [5 +- sq root (97)] / 12

x1 = [5 + </span><span><span><span>9.8488578018 </span> </span> </span> ] / 12
x1 = <span> <span> <span> 14.8488578018 </span> </span> </span> / 12
x1 = <span> <span> <span> 1.2374048168 </span> </span> </span>

x2 = [5 - <span> <span> <span> 9.8488578018 </span> </span> </span> ] / 12
x2 = <span> <span> <span> -4.8488578018 </span> </span> </span> / 12
x2 = <span> <span> <span> -0.4040714835 </span> </span> </span>


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<h3><u>Explanation</u><u>:</u></h3>
  • Calculate the slope with two given coordinate points by using rise over run.

m =  \frac{y_2 - y_1}{x_2 - x_1}

Let these points

\begin{cases}(x_1, y_1) = ( - 4,  - 1) \\ (x_2, y_2) = ( 2,  8) \end{cases}

m =  \frac{8 - ( - 1)}{2 - ( - 4)}  \\ m =  \frac{8 + 1}{2 + 4}  \Longrightarrow \frac{9}{6}  \Longrightarrow \frac{3}{2}  \\ m =  \frac{3}{2}

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y = mx + b \\ m = slope \\ b = y - intercept

Substitute the value of m in the equation.

y =  \frac{3}{2} x + b

  • Substitute any coordinate points that are given or part of the graph in the equation.

(x_, y) = ( - 4,  - 1)

- 1 =  \frac{3}{2} ( - 4) + b

  • Solve the equation for b-term.

- 1 =  \frac{3}{ \cancel{2}} ( \cancel{ - 4})   + b\\  - 1 = 3( - 2) + b \\  - 1 =  - 6 + b \\  - 1 + 6 = b \\ 5 = b

  • Rewrite the equation by substituting the value of b in the equation.

y =  \frac{3}{2} x + 5

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

\large \boxed{y =  \frac{3}{2} x + 5}

<em>If</em><em> </em><em>you</em><em> </em><em>have</em><em> </em><em>any</em><em> </em><em>questions</em><em> </em><em>related</em><em> </em><em>to</em><em> </em><em>the</em><em> </em><em>answer</em><em>,</em><em> </em><em>feel</em><em> </em><em>free</em><em> </em><em>to</em><em> </em><em>ask</em><em> </em><em>via</em><em> </em><em>comment</em><em>.</em>

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Answer:

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