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4 years ago

Identify any solutions to the system given below. 2x + y = 5 3y = 15 – 6x (6, –7) (2, 1) (–2, –9) (–4, 13)

Mathematics

2 answers:

sashaice [31]4 years ago

8 0

Answer:

The answer (2, 1), (-4,13), (6,-7)

Step-by-step explanation:

Consider 2x+y=5 as equation 1, and 3y=15-6x as equation 2

1. Substituting values x and y with x=2 and y=1 as given by the coordinates (2,1)

Equation 1

2(2)+1=5 therefor it holds

Equation 2

3(1)=15-(6×2) also holds

2. Substituting values x and y with x=6 and y=-7 as given by the coordinates (6,-7)

Equation 1

2(6)+(-7)=5

5=5 holds

Equation 2

3(-7)=15-(6×6)

-21=-21 also holds

3. Substituting values x and y with x=-4 and y=13 as given by the coordinates (-4,13)

Equation 1

2(-4)+13=13-8=5 holds

Equation 2

3(13)=15-(6×-4)=39 also holds

4. Substituting values x and y with x=-2 and y=-9 as given by the coordinates (-2,-9)

Equation 1

2(-2)+(-9)=-4-9=-13≠5 does not hold

Equation 2

3(-9)≠15-(6×-2)

-27≠27 does not hold

The coordinates (2,1), (-4,13) and (6,-7) can be used as solutions to the system given

fomenos4 years ago

8 0

Answer:

(6,-7) (2,1) (-4,13)

Step-by-step explanation:

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Multiple Choice

WINSTONCH [101]

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Answer:

B. P = 70 in; A = 300 in²

Step-by-step explanation:

The perimeter is the sum of the side lengths. Opposite sides are the same length, so the perimeter is ...

P = 20 in + 15 in + 20 in + 15 in = 2(20 in +15 in) = 2(35 in)

P = 70 in.

Only answer choice B has the correct value. (Its area figure is also correct.)

7 0

3 years ago

SOMEONE HELP ???? Select steps that could be used to solve the equation 1+ 3x = -x+4

Alex

Answer:

a) add x , subtract 1 and divide by 4

The solution of given equation $x = \frac{3}{4}$

Step-by-step explanation:

Given equation 1+3 x = -x +4

Add 'x' on both sides , we get

1 + 3 x + x = - x + x +4

1 + 4 x = 4

Subtract '1' on both sides , we get

1+4 x -1 = 4 -1

4 x = 3

Dividing '4' on both sides, we get

$\frac{4x}{4} = \frac{3}{4}$

$x = \frac{3}{4}$

Final answer:-

The solution of given equation $x = \frac{3}{4}$

5 0

3 years ago

X/-2=10 (one step equations )

kiruha [24]

$\frac{x}{ - 2} = 10 \\ \: x = - 20$

3 0

3 years ago

Read 2 more answers

Determine the longest side in ΔDEF.

Helen [10]

Option D:

Segment DF

Solution:

Let us first define the relationship between the side and angle in triangle.

Relationship between the side and angle in triangle:

The shortest side is always opposite to the smallest interior angle.
The largest side is always opposite to the largest interior angle.

To find the largest side in ΔDEF:

Largest angle in ΔDEF is ∠E = 73°

So, the side opposite to 73° is DF.

Therefore, Option D is the correct answer.

Hence the segment DF is the longest side in the ΔDEF.

6 0

3 years ago

Read 2 more answers

7. Which of the following can be determined from the graph below?

tatyana61 [14]

Answer:

The ordered pair (6,25) is a solution to both

$y=-\frac{5}{2}x+40$ and $y=\frac{5}{3}x+15$

Step-by-step explanation:

Part 7)

step 1

Find the equation of the line with positive slope

take the points (0,15) and (9,30)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the given values

$m=\frac{30-15}{9-0}$

$m=\frac{15}{9}$

simplify

$m=\frac{5}{3}$

Find the equation of the line in slope intercept form

$y=mx+b$

we have

$m=\frac{5}{3}$

$b=15$

substitute

$y=\frac{5}{3}x+15$

step 2

Find the equation of the line with negative slope

take the points (0,40) and (8,20)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the given values

$m=\frac{20-40}{8-0}$

$m=-\frac{20}{8}$

simplify

$m=-\frac{5}{2}$

Find the equation of the line in slope intercept form

$y=mx+b$

we have

$m=-\frac{5}{2}$

$b=40$

substitute

$y=-\frac{5}{2}x+40$

step 3

Find the solution of the system

we know that

The solution of the system of equations is the intersection point both graphs

The intersection point is (6,25) ----> see the graph

therefore

The ordered pair (6,25) is a solution to both $y=-\frac{5}{2}x+40$ and

$y=\frac{5}{3}x+15$

7 0

4 years ago