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2 years ago

12x + 15y = 9−12x − 18y = −6 PLEASE I NEED EXPLANATION THANKS

Mathematics

1 answer:

Rama09 [41]2 years ago

7 0

Answer:

x = 2

y = –1

Step-by-step explanation:

We need to solve this system of equations for the point where the two linear equations intersect. That means solving for one variable, then using that to solve for the other. But, I'm looking at this, and...

Well, I see an easy way to isolate y right now! See how one equation has 12x and the other has –12x? Adding the two equations together will cancel them out!

That gives us this equation:

12x – 12x + 15y – 18y = 9 – 6 — adding the expressions together

15y – 18y = 9 – 6 — cancel out the 12x

–3y = 3 — simplify the equation

–3y ÷ 3 = 3 ÷ 3 — divide by 3 to isolate y

y = –1 — simplify the equation

Now that we have our y-value, we can substitute into the equation and solve for x. I'm substituting into both to make sure y = –1 is part of the solution point (on a coordinate plane, this is where the functions intersect).

12x + 15y = 9 — original equation

12x + 15(–1) = 9 — substitute –1 for y

12x – 15 = 9 — simplify

12x – 15 + 15 = 9 + 15 — add 15 on both sides to isolate 12x

12x = 24 — simplify

12x ÷ 12 = 24 ÷ 12 — divide by 12 on both sides to isolate x

x = 2 — simplify

That's one equation. Let's check the other with these values to make sure (2, –1) is the solution point.

–12x – 18y = –6

–12(2) – 18(–1) ≟ –6

18 – 24 ≟ –6

–6 = –6 ✓

Yep, this is the solution we're looking for!

Hope this helps you understand the concept! Have a great day!

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2 years ago

Read 2 more answers

Need help Pls explain

Crank

Given:

The graph of a line.

To find:

The equation of the line.

Solution:

From the given graph, it is clear that the line passes through the points (0,-2) and (-6,8). So, the equation of the line is:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-(-2)=\dfrac{8-(-2)}{-6-0}(x-0)$

$y+2=\dfrac{10}{-6}x$

$y+2=-\dfrac{5}{3}x$

Subtract 2 from both sides.

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

Therefore, the equation of the line is $y=-\dfrac{5}{3}x-2$ .

7 0

3 years ago

A square mirror has sides measuring 2 ft less than the sides of a square painting. If the difference between their areas is 32 f

kari74 [83]

Answer: The side lengths of mirror and painting are 7 ft and 9 ft respectively.

Step-by-step explanation: Given that a square mirror has sides measuring 2 ft less than the sides of a square painting and the difference between their areas is 32 ft.

We are to find the lengths of the sides of the mirror and the painting.

Let x ft represents the length of the side of mirror. Then, the side length of square painting is (x+2) ft.

According to the given information, we have

$\textup{area of painting}-\textup{area of mirror}=32\\\\\Rightarrow (x+2)^2-x^2=32\\\\\Rightarrow x^2+4x+4-x^2=32\\\\\Rightarrow 4x=28\\\\\Rightarrow x=\dfrac{28}{4}\\\\\Rightarrow x=7.$

Therefore, the side length of mirror is 7 ft and the side length of painting is (7+2) = 9 ft.

Thus, the side lengths of mirror and painting are 7 ft and 9 ft respectively.

5 0

3 years ago

15 points and brainliest!! please help !!

Arte-miy333 [17]

This will be solved by solving for x first. Firstly you multiply the top equation by 2 and the bottom by -3. This will change both equation to (top)-10x+6y=-54 and (bottom) 27x-6y=-57. Now when you add the factors the y-values cancel out leaving you with; 17x=-3. now you have to divide by 17 on both sides giving you x=-0.17647058823 (not the prettiest solution but you can round if you want to). After that pick an equation to solve for y (I'm picking the top); the equation will be 5(-0.17647058823)+3y=-27. multiply the negative decimal and 5 to get -0.88235294117 (again not the prettiest). Add that to both sides which will give you 3y=-26.1176470588. After this divide both sides by 3 which will give you y=-8.70588235294. Your answer is (-0.17647058823,-8.70588235294) You can divide to the second or third decimal if needed-----remember that as you round from left to right on a decimal if it's below five you leave it and if it's above 5 then round up 1. I hope this help :)

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3 years ago

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kykrilka [37]

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