All categories

2 years ago

For each value of y, determine whether it is a solution to -2y+75-5. Is it a solution?

Mathematics

1 answer:

ser-zykov [4K]2 years ago

3 0

Answer:

• No

• Yes

• No

Step-by-step explanation:

To determine if the 4 given values of y are solutions to the inequality, start by solving the inequality. Solving an inequality is just like that of an equation, except that the direction of the sign changes when the inequality is divided by a negative number.

-2y +7≤ -5

Subtract 7 on both sides:

-2y≤ -5 -7

-2y≤ -12

Divide by -2 on both sides:

y≥ 6

This means that the solution can be 6 or greater than 6.

-10 and 3 are smaller than 6 and are not a solutions, while 7 and 6 satisfies the inequality and are therefore solutions.

_______

Alternatively, we can also substitute each value of y into the inequality and check if the value is less than or equal to -5.

Here's an example to check if -10 is a solution.

-2y +7≤ -5

When y= -10,

-2y +7

= -2(-10) +7

= 20 +7

= 27

Since 27 is greater than 5, it is not a solution to the inequality.

You might be interested in

For which system of equations is (5, 3) the solution? A. 3x – 2y = 9 3x + 2y = 14 B. x – y = –2 4x – 3y = 11 C. –2x – y = –13 x

Alla [95]

The correct answer is:

D) $\left \{ {{2x-y=7} \atop {2x+7y=31}} \right.$ .

Explanation:

We solve each system to find the correct answer.

For A:
$\left \{ {{3x-2y=9} \atop {3x+2y=14}} \right.$

Since we have the coefficients of both variables the same, we will use elimination to solve this.

Since the coefficients of y are -2 and 2, we can add the equations to solve, since -2+2=0 and cancels the y variable:
$\left \{ {{3x-2y=9} \atop {+(3x+2y=14)}} \right. 
\\
\\6x=23$

Next we divide both sides by 6:
6x/6 = 23/6
x = 23/6

This is not the x-coordinate of the answer we are looking for, so A is not correct.

For B:
$\left \{ {{x-y=-2} \atop {4x-3y=11}} \right.$

For this equation, it will be easier to isolate a variable and use substitution, since the coefficient of both x and y in the first equation is 1:
x-y=-2

Add y to both sides:
x-y+y=-2+y
x=-2+y

We now substitute this in place of x in the second equation:
4x-3y=11
4(-2+y)-3y=11

Using the distributive property, we have:
4(-2)+4(y)-3y=11
-8+4y-3y=11

Combining like terms, we have:
-8+y=11

Add 8 to each side:
-8+y+8=11+8
y=19

This is not the y-coordinate of the answer we're looking for, so B is not correct.

For C:
Since the coefficient of x in the second equation is 1, we will use substitution again.

x+2y=-11

To isolate x, subtract 2y from each side:
x+2y-2y=-11-2y
x=-11-2y

Now substitute this in place of x in the first equation:
-2x-y=-13
-2(-11-2y)-y=-13

Using the distributive property, we have:
-2(-11)-2(-2y)-y=-13
22+4y-y=-13

Combining like terms:
22+3y=-13

Subtract 22 from each side:
22+3y-22=-13-22
3y=-35

Divide both sides by 3:
3y/3 = -35/3
y = -35/3

This is not the y-coordinate of the answer we're looking for, so C is not correct.

For D:
Since the coefficients of x are the same in each equation, we will use elimination. We have 2x in each equation; to eliminate this, we will subtract, since 2x-2x=0:

$\left \{ {{2x-y=7} \atop {-(2x+7y=31)}} \right. 
\\
\\-8y=-24$

Divide both sides by -8:
-8y/-8 = -24/-8
y=3

The y-coordinate is correct; next we check the x-coordinate Substitute the value for y into the first equation:
2x-y=7
2x-3=7

Add 3 to each side:
2x-3+3=7+3
2x=10

Divide each side by 2:
2x/2=10/2
x=5

This gives us the x- and y-coordinate we need, so D is the correct answer.

7 0

3 years ago

What is the order of operation for 2(9 + 7)?

shepuryov [24]

the answer is 32 because you add 9 plus 7 then you multiply tha th # by 2

6 0

3 years ago

Read 2 more answers

I need help with this please

Levart [38]

Yu can you think how many triangles fit in that parallelogram? The answer is six. four in the central rectangle and two at the ends, then the area of the parallelogram will be six times greater than that of the triangle in that graph. Good luck! M.

7 0

3 years ago

A line passes through (10,5) and (13,-4). Write the equation of the line in standard form.

nexus9112 [7]

Using two point form
y-5/-4-5=x-10/13-10
rearrange to get 3x+y-35=0

4 0

2 years ago

The marijority of the population in the United states _________.

Nadusha1986 [10]

It should be C english :)

6 0

2 years ago