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3 years ago

What is the value of x in the following system? y = 3x - 5 6x + 3y = 15

Mathematics

1 answer:

aivan3 [116]3 years ago

5 0

Answer:

x = 2

Step-by-step explanation:

I used the process of substitution to do this.

1. put both equations into slope-intercept form:

y = 3x - 5

y = -2x + 5

2. since they both equal y, they must equal each other:

3x - 5 = -2x + 5

3. simplify:

2 = x

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horsena [70]

Answer:

1. (7,-9)

2. (4,0) and (10,0)

3. (3,0) and (-3,0)

4. (0,-9)

5. (-1,-32)

Step-by-step explanation:

To find the vertex use the formula

$\frac{-b}{2a}$

First make the equation into a quadratic equation.

$(x-4)(x-10)\\x^{2} -10x-4x+40\\x^{2} -14x+40$

Now it is in the form

$ax^{2} +bx+c=0$

Now we can substitute the values

$\frac{-(-14)}{2(1)} \\\frac{14}{2} \\7$

Now we have 7 as our x value for the vertex we can substitute for y,

$x^{2} -14x+40=y\\(7)^{2} -14(7)+40=y\\49-98+4=y\\y=-9$

So the vertex for 1 is (7,-9)

To find the intercepts for 2 & 3, they basically already give it to you. You just need to find a value for x for x-4 that will equal it to 0 and another for x for x-10 that will equal it to 0.

$x-4=0\\x=4\\\\x-10=0\\x=10$

4 is slightly different but start the same,

$(x-3)(x+3)\\x^{2}+3x-3x-9\\x^{2}-9$

Here, c (9) just shows the graph move down 9, so the y intercept = 9.

5 is the same process as 1,

$2(x-3)(x+5)\\2(x^{2}+5x-3x-15)\\2(x^{2}+2x-15)\\2x^{2}+4x-30$

Vertex,

$\frac{-(4)}{2(2)} \\\frac{-4}{4} \\-1$

Substitute,

$2x^{2}+4x-30\\2(-1)^{2}+4(-1)-30\\2-4-30\\-32$

So the vertex is (-1,-32)

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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