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2 years ago

How would i solve

1 answer:

3 0

To use the elimination method, the coefficient of one variable in one equation must be the opposite number of the coefficient of the same variable in the second equation.

$4x-3y=8 \\
5x-2y=-11$

Here you can multiply the first equation by 2, and the second equation by -3.

$4x-3y=8 \ \ |\cdot 2 \\
5x-2y=-11 \ \ |\cdot (-3) \\ \\
8x-6y=16 \\
-15x+6y=33$

Now you just add the equations by sides and solve for one variable.

$8x-6y=16 \\ \underline{-15x+6y=33 } \\
8x-6y-15x+6y=16+33 \\
8x-15x=16+33 \\
-7x=49 \\
x=-7$

Now you solve for the other variable by substituting -7 for x in one of the equations.

$4x-3y=8 \\
4 \cdot (-7)-3y=8 \\
-28-3y=8 \\
-3y=8+28 \\
-3y=36 \\
y=-12$

You could choose x at the beginning as well. Then you'd have:
$4x-3y=8 \ \ |\cdot (-5)\\
5x-2y=-11 \ \ |\cdot 4 \\ \\
-20x+15y=-40 \\
\underline{20x-8y=-44 \ \ \ \ \ \ } \\
-20x+15y+20x-8y=-40-44 \\
15y-8y=-40-44 \\
7y=-84 \\
y=-12 \\ \\
4x-3y=8 \\
4x-3 \cdot (-12)=8 \\
4x+36=8 \\
4x=8-36 \\
4x=-28 \\
x=-7$

So the answer is:
$x=-7 \\ y=-12$

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a fruit delivers its fruit in two types of boxes: large and small. a delivery of 3 large boxes and 5 small boxes has a total wei

Masteriza [31]

Answer:

The weight of a small box = 13.5 kg

The weight of 1 large box = 18.5 kg

Step-by-step explanation:

Let us assume the weight of a small box = m kg

And the weight of 1 large box = n kg

Now, the weight of 5 small box = 5 x (weight of 1 small box) = 5 m

Also, the weight of 3 large box = 3 x (weight of 1 large box) = 3 n

Here, 3 large boxes + 5 small boxes = of 123 kilograms

⇒ 5 m + 3 n = 123 .... (1)

Again, the weight of 2 small box = 2 x (weight of 1 small box) = 2 m

Also, the weight of 12 large box = 12 x (weight of 1 large box) = 12 n

Here, 12 large boxes + 2 small boxes = 249 kilograms

⇒ 2 m+ 12 n = 249 .... (2)

Now, solving both the given equations by ELIMINATION, we get:

5 m + 3 n = 123 x (2)

2 m+ 12 n = 249 x (-5)

we get the new set of equitation as:

10 m + 6 n = 246

- 10 m - 60 n = -1245

Adding both equation, we get

-54 n = 999

or, n = 18.5

Now, 5 m + 3 n = 123

So, 5 m = 123 -3 (18.5) = 123 - 55.5 = 67.5

⇒ m = 13.5

Hence, the weight of a small box = m kg = 13.5 kg

And the weight of 1 large box = n kg = 18.5 kg

8 0

2 years ago

Help very fast please help me

Irina18 [472]

Find the discount price and subtract from the total to find the sale price.

To find the discount price, multiply 90 b 40% (convert 40% into decimal)

90 x 0.4 = 36

Next, subtract the discount from the total to find the sale price.

90 - 36 = 54

So, the sale price is <u>$54</u>.

6 0

2 years ago

The problem is in the picture :)

frozen [14]

Answer:

Last option: 4

Step-by-step explanation:

The quadratic equation simplified: $x^2-4x=-\frac{7}{2}$ has the form:

$ax^2+bx=c$

In this case, you can identify that "a", "b" and "c" are:

$a=1\\b=-4\\c=-\frac{7}{2}$

To solve this quadratic equation by completing the square, Carlos should add $(\frac{b}{2})^2$ to both sides of the equation. This is:

$(\frac{-4}{2})^2=(-2)^2=4$

Then:

$x^2-4x+4=-\frac{7}{2}+4$

Therefore you can observe that the number he should add to both sides of the equation is: 4

8 0

2 years ago

Find the volume for each rectangular prism

Elden [556K]

Answer: 385 cm

Step-by-step explanation: V= l*w*h

V= 7*5*11

= 385

6 0

3 years ago

Read 2 more answers

A submarine sits at -300 meters in relation to sea level. Then it descends 115 meters. What is it’s new position in relation to

Anna71 [15]

Answer:

A. -415m

Step-by-step explanation:

-300 meters is the starting point.

Then, the submarine goes 115m further below the surface, which can be represented as -115.

Add -300 and -115 and you get -415m.

3 0

3 years ago