If R = { (x, y) is an element of N, x is an element of N, y is an element of N / x-y is divisible by 5 } then show that R is an
1 answer:
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The <u>correct answer</u> is:
D)
.
Explanation:
We solve each system to find the correct answer.
<u>For A:</u>
Since we have the coefficients of both variables the same, we will use <u>elimination </u>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:
Next we divide both sides by 6:
6x/6 = 23/6
x = 23/6
This is <u>not the x-coordinate</u> of the answer we are looking for, so <u>A is not correct</u>.
<u>For B</u>:
For this equation, it will be easier to isolate a variable and use <u>substitution</u>, 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 <u>not the y-coordinate</u> of the answer we're looking for, so <u>B is not correct</u>.
<u>For C</u>:
Since the coefficient of x in the second equation is 1, we will use <u>substitution</u> 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 <u>not the y-coordinate</u> of the answer we're looking for, so <u>C is not correct</u>.
<u>For D</u>:
Since the coefficients of x are the same in each equation, we will use <u>elimination</u>. We have 2x in each equation; to eliminate this, we will subtract, since 2x-2x=0:
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 <u>D is the correct answer</u>.
D)
Explanation:
We solve each system to find the correct answer.
<u>For A:</u>
Since we have the coefficients of both variables the same, we will use <u>elimination </u>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:
Next we divide both sides by 6:
6x/6 = 23/6
x = 23/6
This is <u>not the x-coordinate</u> of the answer we are looking for, so <u>A is not correct</u>.
<u>For B</u>:
For this equation, it will be easier to isolate a variable and use <u>substitution</u>, 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 <u>not the y-coordinate</u> of the answer we're looking for, so <u>B is not correct</u>.
<u>For C</u>:
Since the coefficient of x in the second equation is 1, we will use <u>substitution</u> 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 <u>not the y-coordinate</u> of the answer we're looking for, so <u>C is not correct</u>.
<u>For D</u>:
Since the coefficients of x are the same in each equation, we will use <u>elimination</u>. We have 2x in each equation; to eliminate this, we will subtract, since 2x-2x=0:
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 <u>D is the correct answer</u>.