All categories

2 years ago

Y = -3x +10 3x +y = 5 substitution method

Mathematics

1 answer:

spayn [35]2 years ago

3 0

Answer:

no solutions

Step-by-step explanation:

y = -3x +10

3x +y = 5

Substitute the first equation into the second equation

Let every instance of y in the second equation be replaced with -3x+10

3x+ (-3x+10) = 5

Combine like terms

10 =5

This is never true so there are no solutions

(These are parallel lines with the same slope but different y intercepts)

You might be interested in

2x2 – 5x + 67 = 0<br> What would be your first step in completing the square for the equation above?

7nadin3 [17]

Answer:

The first step is to divide all the terms by the coefficient of $x^{2}$ which is 2.

The solutions to the quadratic equation $2x^2\:-\:5x\:+\:67\:=\:0$ are:

$x=\frac{5}{4}+i\frac{\sqrt{511}}{4},\:x=\frac{5}{4}-i\frac{\sqrt{511}}{4}$

Step-by-step explanation:

Considering the equation

$2x^2\:-\:5x\:+\:67\:=\:0$

The first step is to divide all the terms by the coefficient of $x^{2}$ which is 2.

$\frac{2x^2-5x}{2}=\frac{-67}{2}$

$x^2-\frac{5x}{2}=-\frac{67}{2}$

Lets now solve the equation by completeing the remaining steps

Write equation in the form: $x^2+2ax+a^2=\left(x+a\right)^2$

Solving for $a$ ,

$2ax=-\frac{5}{2}x$

$a=-\frac{5}{4}$

$\mathrm{Add\:}a^2=\left(-\frac{5}{4}\right)^2\mathrm{\:to\:both\:sides}$

$x^2-\frac{5x}{2}+\left(-\frac{5}{4}\right)^2=-\frac{67}{2}+\left(-\frac{5}{4}\right)^2$

$x^2-\frac{5x}{2}+\left(-\frac{5}{4}\right)^2=-\frac{511}{16}$

Completing the square

$\left(x-\frac{5}{4}\right)^2=-\frac{511}{16}$

Since, you had required to know the first step in completing the square for the equation above, I hope you have got the point, but let me quickly solve the remaining solution.

For $f^2\left(x\right)=a$ the solution are $f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

Solving

$x-\frac{5}{4}=\sqrt{-\frac{511}{16}}$

$x-\frac{5}{4}=\sqrt{-1}\sqrt{\frac{511}{16}}$

$x-\frac{5}{4}=i\sqrt{\frac{511}{16}}$ ∵ Applying imaginary number rule $\sqrt{-1}=i$

$x-\frac{5}{4}=i\frac{\sqrt{511}}{\sqrt{16}}$

$-\frac{5}{4}=i\frac{\sqrt{511}}{4}$

$x=\frac{5}{4}+i\frac{\sqrt{511}}{4}$

Similarly, solving

$x-\frac{5}{4}=-\sqrt{-\frac{511}{16}}$

$x-\frac{5}{4}=-i\frac{\sqrt{511}}{4}$ ∵ Applying imaginary number rule $\sqrt{-1}=i$

$x=\frac{5}{4}-i\frac{\sqrt{511}}{4}$

Therefore, the solutions to the quadratic equation are:

$x=\frac{5}{4}+i\frac{\sqrt{511}}{4},\:x=\frac{5}{4}-i\frac{\sqrt{511}}{4}$

4 0

2 years ago

Find LCM of 7 and 13

ella [17]

7=7×1 13=13×1 Lcm=7×13 =91

5 0

3 years ago

A square room has a tiled floor with 144 tiles. How many tiles are along the edge?

pentagon [3]

36
This is because its a square shape so you would divide 144 by 4 and you get 36

I hope this helps:)

6 0

2 years ago

Evaluate 5(x-1)-2when x=3

Ugo [173]

Answer:

Step-by-step explanation:

5(x-1)-2

5(2-1)-2

5×1-2

5-2

Hope this helps you :)

please mark brainliest

6 0

3 years ago

Read 2 more answers

Some help me please

const2013 [10]

Answer:

Step-by-step explanation:

Horrible writing JK have a good day :)

5 0

3 years ago

Read 2 more answers