All categories

4 years ago

Which ordered pair (a, b) is a solution to the given system? {2a - 5b=1] {3a+5b=14}

Mathematics

2 answers:

Aleonysh [2.5K]4 years ago

8 0

Answer:

(3,-1)

Step-by-step explanation:

$2a - 5b=1 \ and \ 3a+5b=14$

WE use elimination method to solve for a and b

$2a - 5b=1$

$3a+5b=14$

---------------------------------

$5a=15$

Divide by 5 on both sides

a = 3

Now plug in a=3 in first equation

$2a-5b=1$

$2(3)-5b=1$

$6-5b=1$

Subtract 6 on both sides

5b=-5 ( divide by 5 on both sides)

b = -1

Ordered pair is (3,-1)

Schach [20]4 years ago

5 0

A = 3, b = -1, it's easier to use elimination to solve for a since the coefficients for the two b's are the same number.

You might be interested in

Graph the equation below by plotting the y-intercept and a second point on the line. When you click Done, your line will appear

Gala2k [10]

Answer:

Step-by-step explanation:

Equation of the line has been given as,

$y=\frac{3}{2}x-5$

By comparing this equation with the y-intercept form of the equation,

y = mx + b

Slope of the line 'm' = $\frac{3}{2}$

and y-intercept 'b' = -5

Table for the points to be plotted on a graph will be,

x y

-4 -11

-2 -6

0 -5

2 -4

4 -3

By plotting y-intercept (0, -5) and any one of the points given in the table we can get the required line.

5 0

3 years ago

GIVING OUT BRAINLIEST TO WHOEVER GETS ALL OF THEM RIGHT

Thepotemich [5.8K]

Answer:

4) $\frac{x}{7\cdot x +x^{2}}$ is equivalent to $\frac{1}{7+x}$ for all $x \ne -7$ . (Answer: A)

5) $\frac{-14\cdot x^{3}}{x^{3}-5\cdot x^{4}}$ is equivalent to $-\frac{14}{1-5\cdot x}$ for all $x \ne \frac{1}{5}$ . (Answer: B)

6) $\frac{x+7}{x^{2}+4\cdot x - 21}$ is equivalent to $\frac{1}{x-3}$ for all $x \ne 3$ . (Answer: None)

7) $\frac{x^{2}+3\cdot x -4}{x+4}$ is equivalent to $x - 1$ . (Answer: None)

8) $\frac{2}{3\cdot a}\cdot \frac{2}{a^{2}}$ is equivalent to $\frac{4}{3\cdot a^{3}}$ for all $a\ne 0$ . (Answer: A)

Step-by-step explanation:

We proceed to simplify each expression below:

4) $\frac{x}{7\cdot x +x^{2}}$

(i) $\frac{x}{7\cdot x +x^{2}}$ Given

(ii) $\frac{x}{x\cdot (7+x)}$ Distributive property

(iii) $\frac{1}{7+x} \cdot \frac{x}{x}$ Distributive property

(iv) $\frac{1}{7+x}$ Existence of multiplicative inverse/Modulative property/Result

Rational functions are undefined when denominator equals 0. That is:

$7+x = 0$

$x = -7$

Hence, we conclude that $\frac{x}{7\cdot x +x^{2}}$ is equivalent to $\frac{1}{7+x}$ for all $x \ne -7$ . (Answer: A)

5) $\frac{-14\cdot x^{3}}{x^{3}-5\cdot x^{4}}$

(i) $\frac{-14\cdot x^{3}}{x^{3}-5\cdot x^{4}}$ Given

(ii) $\frac{x^{3}\cdot (-14)}{x^{3}\cdot (1-5\cdot x)}$ Distributive property

(iii) $\frac{x^{3}}{x^{3}} \cdot \left(-\frac{14}{1-5\cdot x} \right)$ Distributive property

(iv) $-\frac{14}{1-5\cdot x}$ Commutative property/Existence of multiplicative inverse/Modulative property/Result

Rational functions are undefined when denominator equals 0. That is:

$1-5\cdot x = 0$

$5\cdot x = 1$

$x = \frac{1}{5}$

Hence, we conclude that $\frac{-14\cdot x^{3}}{x^{3}-5\cdot x^{4}}$ is equivalent to $-\frac{14}{1-5\cdot x}$ for all $x \ne \frac{1}{5}$ . (Answer: B)

6) $\frac{x+7}{x^{2}+4\cdot x - 21}$

(i) $\frac{x+7}{x^{2}+4\cdot x - 21}$ Given

(ii) $\frac{x+7}{(x+7)\cdot (x-3)}$ $x^{2} -(r_{1}+r_{2})\cdot x +r_{1}\cdot r_{2} = (x-r_{1})\cdot (x-r_{2})$

(iii) $\frac{1}{x-3}\cdot \frac{x+7}{x+7}$ Commutative and distributive properties.

(iv) $\frac{1}{x-3}$ Existence of multiplicative inverse/Modulative property/Result

Rational functions are undefined when denominator equals 0. That is:

$x-3 = 0$

$x = 3$

Hence, we conclude that $\frac{x+7}{x^{2}+4\cdot x - 21}$ is equivalent to $\frac{1}{x-3}$ for all $x \ne 3$ . (Answer: None)

7) $\frac{x^{2}+3\cdot x -4}{x+4}$

(i) $\frac{x^{2}+3\cdot x -4}{x+4}$ Given

(ii) $\frac{(x+4)\cdot (x-1)}{x+4}$ $x^{2} -(r_{1}+r_{2})\cdot x +r_{1}\cdot r_{2} = (x-r_{1})\cdot (x-r_{2})$

(iii) $(x-1)\cdot \left(\frac{x+4}{x+4} \right)$ Commutative and distributive properties.

(iv) $x - 1$ Existence of additive inverse/Modulative property/Result

Polynomic function are defined for all value of $x$ .

$\frac{x^{2}+3\cdot x -4}{x+4}$ is equivalent to $x - 1$ . (Answer: None)

8) $\frac{2}{3\cdot a}\cdot \frac{2}{a^{2}}$

(i) $\frac{2}{3\cdot a}\cdot \frac{2}{a^{2}}$

(ii) $\frac{4}{3\cdot a^{3}}$ $\frac{a}{b}\cdot \frac{c}{d} = \frac{a\cdot b}{c\cdot d}$ /Result

Rational functions are undefined when denominator equals 0. That is:

$3\cdot a^{3} = 0$

$a = 0$

Hence, $\frac{2}{3\cdot a}\cdot \frac{2}{a^{2}}$ is equivalent to $\frac{4}{3\cdot a^{3}}$ for all $a\ne 0$ . (Answer: A)

6 0

3 years ago

PLEASE HELP I SET TO 14 POINTS AND WILL MARK BRAINLEST❤️ thank youuu!

andriy [413]

Hello! First we should note that the shape of the figure can be broken down into two rectangular prisms, so that the expression will look like:

Volume = (w • h • l) vertical rectangular prism + (w •h • l) horizontal rectangular prism

Thus Volume = (7 • 3 • 3) + (9 • 3 • 4)

6 0

3 years ago

Read 2 more answers

What is the quadratic equation of x2 - 7x + 6 = 0

s2008m [1.1K]

Answer:

x = 6 , 1

Step-by-step explanation:

7 0

3 years ago

A blimp is flying at a speed of 40mph and going in a direction of 80 degrees. After 3 hours of flying it turns and travels 1 hou

kykrilka [37]

Bearing is a topic that can be used to locate the position of an object at a given time. Therefore, the blimp is 80 m far away from its starting point. And in the North-East direction.

The speed of an object relates the distance it covers to the time taken to cover the said distance.

i.e speed = $\frac{distance}{time taken}$