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2 years ago

Solve the system by substitution.

Mathematics

1 answer:

kirill [66]2 years ago

8 0

<h2>Answer:</h2>

x = 1

y = 1

<h3>Step-by-step explanation:</h3>

$y=-3x+4\\ y=x$

Substitute into one of the equations

$-3x+4=x$

Rearrange variables to the left sider of the equation

$-3x-x=-4$

Combine like terms

$-4x=-4$

Divide both sides of the equation by the coefficient of variable

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

Determine the sign for multiplication or division

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

Cross out the common factor

$x=1$

Substitute into one of the equations

$y=1$

The solution of the system is

$\left \{ {{x=1} \atop {y=1}} \right.$

<em>I hope this helps you</em>

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Find four consecutive even integers whose sum is 84. Find the integers.

mina [271]

Suppose the integers are n , n+2 , n+4 and n+6.
84=n+(n+2)+(n+4)+(n+6)=4n+12.
Subtract 12 from both ends to get.
72=4n.
Divide both ends by 4 to get.
n=18.
So the integers are: 18 , 20 , 22 , 24.

4 0

3 years ago

How many pounds of cashews that cost $14 per pound must be mixed with 5 pounds of peanuts that cost $6.50 per pound to make mixe

Fantom [35]

The amount of cashew mixed is 5 pounds

<h3>Word problem on total cost</h3>

Cost of 1 pound of cashew = $14

Cost of 1 pound of peanut = $6.50

Total cost of 1 pound of the mixed nuts = $10.25

Cost of 5 pounds of peanuts = 5 x $6.50

Cost of 5 pounds of peanuts = $32.50

Let the amount of cashew be x

Total cost of x cashew = 14x

Total amount of the mixed nuts = x + 5

Total cost of the mixed nuts = 10.25(x+5)

Total cost of the mixed nuts = 10.25x + 51.25

14x + 32.50 = 10.25x + 51.25

14x - 10.25x = 51.25 - 32.50

3.75x = 18.75

x = 18.75/3.75

x = 5

Therefore, the amount of cashew mixed is 5 pounds

Learn more on word problem on cost here: brainly.com/question/21405634

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2 years ago

Read 2 more answers

What is the range of the function?

levacccp [35]

Answer:

e equels MC squared

Step-by-step explanation:

7 0

3 years ago

A boat costs $8,350 and decreases in value by 12% per year. how much will the boat be worth after 5 years?

BARSIC [14]

The boat would cost 3,340 dollars

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3 years ago

State whether the lines are parallel, perpendicular,or neither.

cluponka [151]

Answer:

Please check the explanation.

Step-by-step explanation:

Two lines are parallel if their slopes are equal.

Two lines are perpendicular if the product of their slope is -1

We also know that the slope-intercept form of the line equation is

$y=mx+b$

where m is the slope and b is the y-intercept

Given the lines

y = 6х - 3

Comparing with y=mx+b, the slope of y = 6х - 3:

m₁=6

y = - 1/6x + 7

Comparing with y=mx+b, the slope of y = - 1/6x + 7:

m₂=-1/6

m₁ × m₂ = -1

6 × - 1/6 = -1

-1 = -1

Thus, the lines y = 6х - 3 and y = - 1/6x + 7 are perpendicular.

y = 3x + 2

Comparing with y=mx+b, the slope of y = 3x + 2:

m₁=3

2y = 6x - 6

simplifying to write in slope-intercept form

y=3x-3

Comparing with y=mx+b, the slope of y=3x-3:

m₂=3

As the slopes of y = 3x + 2 and 2y = 6x - 6 are equal.

i.e. m₁ = m₂ → 3 = 3

Thus, the lines y = 3x + 2 and 2y = 6x - 6 are paralle.

8x - 2y = 3

simplifying to write in slope-intercept form

y = 4x - 3/2

Comparing with y=mx+b, the slope of y = 4x - 3/2:

m₁=4

x + 4y = - 1

simplifying to write in slope-intercept form

y=-1/4x-1/4

Comparing with y=mx+b, the slope of y=-1/4x-1/4:

m₂=-1/4

m₁ × m₂ = -1

4 × - 1/4 = -1

-1 = -1

Thus, the lines 8x - 2y = 3 and x + 4y = - 1 are perpendicular.

3x+2y = 5

simplifying to write in slope-intercept form

y = -3/2x + 5/2

Comparing with y=mx+b, the slope of y = -3/2x + 5/2:

m₁=-3/2

3y + 2x = - 3

simplifying to write in slope-intercept form

y = -2/3x - 1

Comparing with y=mx+b, the slope of y = -2/3x - 1:

m₂=-2/3

As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.

y - 5 = 6x

simplifying to write in slope-intercept form

y=6x+5

Comparing with y=mx+b, the slope of y=6x+5:

m₁=6

y - 6x = - 1

simplifying to write in slope-intercept form

y=6x-1

Comparing with y=mx+b, the slope of y=6x-1:

m₂=6

As the slopes of y - 5 = 6x and y - 6x = -1 are equal.

i.e. m₁ = m₂ → 6 = 6

Thus, the lines y - 5 = 6x and y - 6x = -1 are paralle.

y = 3х + 9

Comparing with y=mx+b, the slope of y = 3х + 9:

m₁=3

y = -1/3x - 4

Comparing with y=mx+b, the slope of y = 1/3x - 4:

m₂=1/3

As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.

8 0

2 years ago