Solved on Feb 23, 2024

Identify the ordered pair that does not solve the linear equation $5x + y = 10$ .

STEP 1

Assumptions
1. The given linear equation is $5x + y = 10$ .
2. We have four ordered pairs to check: $(-3, 20)$ , $(1, 5)$ , $(0, 10)$ , and $(2, 0)$ .
3. We need to determine which ordered pair does not satisfy the given linear equation.

STEP 2

To check if an ordered pair $(x, y)$ is a solution to the linear equation $5x + y = 10$ , we will substitute the values of $x$ and $y$ into the equation and see if the equation holds true.

STEP 3

First, we will check the ordered pair $(-3, 20)$ .
Substitute $x = -3$ and $y = 20$ into the equation:
$5(-3) + 20 = 10$

STEP 4

Calculate the left-hand side of the equation with the substituted values:
$5(-3) + 20 = -15 + 20$

STEP 5

Simplify the result:
$-15 + 20 = 5$

STEP 6

Since $5 \neq 10$ , the ordered pair $(-3, 20)$ does not satisfy the equation $5x + y = 10$ .

STEP 7

Next, we will check the ordered pair $(1, 5)$ .
Substitute $x = 1$ and $y = 5$ into the equation:
$5(1) + 5 = 10$

STEP 8

Calculate the left-hand side of the equation with the substituted values:
$5(1) + 5 = 5 + 5$

STEP 9

Simplify the result:
$5 + 5 = 10$

STEP 10

Since $10 = 10$ , the ordered pair $(1, 5)$ satisfies the equation $5x + y = 10$ .

STEP 11

Now, we will check the ordered pair $(0, 10)$ .
Substitute $x = 0$ and $y = 10$ into the equation:
$5(0) + 10 = 10$

STEP 12

Calculate the left-hand side of the equation with the substituted values:
$5(0) + 10 = 0 + 10$

STEP 13

Simplify the result:
$0 + 10 = 10$

STEP 14

Since $10 = 10$ , the ordered pair $(0, 10)$ satisfies the equation $5x + y = 10$ .

STEP 15

Finally, we will check the ordered pair $(2, 0)$ .
Substitute $x = 2$ and $y = 0$ into the equation:
$5(2) + 0 = 10$

STEP 16

Calculate the left-hand side of the equation with the substituted values:
$5(2) + 0 = 10 + 0$

STEP 17

Simplify the result:
$10 + 0 = 10$

STEP 18

Since $10 = 10$ , the ordered pair $(2, 0)$ satisfies the equation $5x + y = 10$ .

STEP 19

We have found that the ordered pair $(-3, 20)$ does not satisfy the equation $5x + y = 10$ , while the other three ordered pairs do satisfy the equation.
The ordered pair that is not a solution to the equation is $(-3, 20)$ .

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Identify the ordered pair that does not solve the linear equation 5x+y=105x + y = 105x+y=10.

STEP 1

Assumptions1. The given linear equation is 5x+y=105x + y = 105x+y=10.2. We have four ordered pairs to check: (−3,20)(-3, 20)(−3,20), (1,5)(1, 5)(1,5), (0,10)(0, 10)(0,10), and (2,0)(2, 0)(2,0).3. We need to determine which ordered pair does not satisfy the given linear equation.

STEP 2

To check if an ordered pair (x,y)(x, y)(x,y) is a solution to the linear equation 5x+y=105x + y = 105x+y=10, we will substitute the values of xxx and yyy into the equation and see if the equation holds true.

STEP 3

First, we will check the ordered pair (−3,20)(-3, 20)(−3,20).Substitute x=−3x = -3x=−3 and y=20y = 20y=20 into the equation:5(−3)+20=105(-3) + 20 = 105(−3)+20=10

STEP 4

Calculate the left-hand side of the equation with the substituted values:5(−3)+20=−15+205(-3) + 20 = -15 + 205(−3)+20=−15+20

STEP 5

Simplify the result:−15+20=5-15 + 20 = 5−15+20=5

STEP 6

Since 5≠105 \neq 105=10, the ordered pair (−3,20)(-3, 20)(−3,20) does not satisfy the equation 5x+y=105x + y = 105x+y=10.

STEP 7

Next, we will check the ordered pair (1,5)(1, 5)(1,5).Substitute x=1x = 1x=1 and y=5y = 5y=5 into the equation:5(1)+5=105(1) + 5 = 105(1)+5=10

STEP 8

Calculate the left-hand side of the equation with the substituted values:5(1)+5=5+55(1) + 5 = 5 + 55(1)+5=5+5

STEP 9

Simplify the result:5+5=105 + 5 = 105+5=10

STEP 10

Since 10=1010 = 1010=10, the ordered pair (1,5)(1, 5)(1,5) satisfies the equation 5x+y=105x + y = 105x+y=10.

STEP 11

Now, we will check the ordered pair (0,10)(0, 10)(0,10).Substitute x=0x = 0x=0 and y=10y = 10y=10 into the equation:5(0)+10=105(0) + 10 = 105(0)+10=10

STEP 12

Calculate the left-hand side of the equation with the substituted values:5(0)+10=0+105(0) + 10 = 0 + 105(0)+10=0+10

STEP 13

Simplify the result:0+10=100 + 10 = 100+10=10

STEP 14

Since 10=1010 = 1010=10, the ordered pair (0,10)(0, 10)(0,10) satisfies the equation 5x+y=105x + y = 105x+y=10.

STEP 15

Finally, we will check the ordered pair (2,0)(2, 0)(2,0).Substitute x=2x = 2x=2 and y=0y = 0y=0 into the equation:5(2)+0=105(2) + 0 = 105(2)+0=10

STEP 16

Calculate the left-hand side of the equation with the substituted values:5(2)+0=10+05(2) + 0 = 10 + 05(2)+0=10+0

STEP 17

Simplify the result:10+0=1010 + 0 = 1010+0=10

STEP 18

Since 10=1010 = 1010=10, the ordered pair (2,0)(2, 0)(2,0) satisfies the equation 5x+y=105x + y = 105x+y=10.

STEP 19

We have found that the ordered pair (−3,20)(-3, 20)(−3,20) does not satisfy the equation 5x+y=105x + y = 105x+y=10, while the other three ordered pairs do satisfy the equation.The ordered pair that is not a solution to the equation is (−3,20)(-3, 20)(−3,20).

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Identify the ordered pair that does not solve the linear equation $5x + y = 10$ .

Assumptions
1. The given linear equation is $5x + y = 10$ .
2. We have four ordered pairs to check: $(-3, 20)$ , $(1, 5)$ , $(0, 10)$ , and $(2, 0)$ .
3. We need to determine which ordered pair does not satisfy the given linear equation.

To check if an ordered pair $(x, y)$ is a solution to the linear equation $5x + y = 10$ , we will substitute the values of $x$ and $y$ into the equation and see if the equation holds true.

First, we will check the ordered pair $(-3, 20)$ .
Substitute $x = -3$ and $y = 20$ into the equation:
$5(-3) + 20 = 10$

Calculate the left-hand side of the equation with the substituted values:
$5(-3) + 20 = -15 + 20$

Simplify the result:
$-15 + 20 = 5$

Since $5 \neq 10$ , the ordered pair $(-3, 20)$ does not satisfy the equation $5x + y = 10$ .

Next, we will check the ordered pair $(1, 5)$ .
Substitute $x = 1$ and $y = 5$ into the equation:
$5(1) + 5 = 10$

Calculate the left-hand side of the equation with the substituted values:
$5(1) + 5 = 5 + 5$

Simplify the result:
$5 + 5 = 10$

Since $10 = 10$ , the ordered pair $(1, 5)$ satisfies the equation $5x + y = 10$ .

Now, we will check the ordered pair $(0, 10)$ .
Substitute $x = 0$ and $y = 10$ into the equation:
$5(0) + 10 = 10$

Calculate the left-hand side of the equation with the substituted values:
$5(0) + 10 = 0 + 10$

Simplify the result:
$0 + 10 = 10$

Since $10 = 10$ , the ordered pair $(0, 10)$ satisfies the equation $5x + y = 10$ .

Finally, we will check the ordered pair $(2, 0)$ .
Substitute $x = 2$ and $y = 0$ into the equation:
$5(2) + 0 = 10$

Calculate the left-hand side of the equation with the substituted values:
$5(2) + 0 = 10 + 0$

Simplify the result:
$10 + 0 = 10$

Since $10 = 10$ , the ordered pair $(2, 0)$ satisfies the equation $5x + y = 10$ .

We have found that the ordered pair $(-3, 20)$ does not satisfy the equation $5x + y = 10$ , while the other three ordered pairs do satisfy the equation.
The ordered pair that is not a solution to the equation is $(-3, 20)$ .