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4 years ago

Solve the system using substitution. Write the solution as an ordered pair. (1 point) SHOW YOUR WORK FOR FULL CREDIT! (2 points)

Mathematics

2 answers:

Darya [45]4 years ago

7 0

Answer:y = -7, x = 12

Step-by-step explanation:

y + x = 5

x = 5 - y

y = 2(5 - y) + 11

y = 10 - 2y +11

-y -y

0 = 10 - 3y + 11

21 = -3y

y = -7

-7 + x = 5

x = 12

beks73 [17]4 years ago

3 0

x = -2

y = 7

Solution: (-2,7)

//Hope this helps.

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475 boats in 3 hours ratio unit per hour

Dovator [93]

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6 0

3 years ago

Two thirds of a number decreased by six is two. what is the number?

Kisachek [45]

Answer: The number is: " 12 ".

____________________________________
Let "x" represent "the unknown number" (for which we wish to solve.

The expression:

$\frac{2}{3}$ x − 6 = 2 ; Solve for "x" ;
_______________________________________________
Method 1)

Add "6" to EACH SIDE of the equation;
_______________________________________________
→ $\frac{2}{3}$ x − 6 + 6 = 2 + 6 ;

to get:

→ $\frac{2}{3}$ x = 8 ;
______________________________________________
Multiply each side of the equation by " $\frac{3}{2}$ " ; to isolate "x" on one side of the equation ; and to solve for "x" ;
______________________________________________
→ $\frac{3}{2}$ * $\frac{2}{3}$ x = 8 * $\frac{3}{2}$ ;

→ x = 8 * $\frac{3}{2}$ ;

= $\frac{8}{1}$ * $\frac{3}{2}$ ;

= $\frac{8*3}{1*2}$ ;

= $\frac{24}{2}$ ;

= 12 .
______________________________________________
x = 12 .
______________________________________________
Method 2)
______________________________________________
$\frac{2}{3}$ x − 6 = 2 ; Solve for "x" ;

Add "6" to EACH SIDE of the equation;
_______________________________________________
→ $\frac{2}{3}$ x − 6 + 6 = 2 + 6 ;

to get:
→ $\frac{2}{3}$ x = 8 ;
______________________________________________
Multiply each side of the equation by "3" ; to get rid of the "fraction" ;
 → 3 * $\frac{2}{3}$ x = 8 * 3 ;
→ $\frac{3}{1}$ * $\frac{2}{3}$ x = 8 * 3 ;
→ $\frac{3*2}{1*3}$ x = 8 * 3
→ $\frac{6}{3}$ x = 24 ;

→ 2x = 24 ;

→ Divide each side of the equation by "2" ; to isolate "x" on one side of the equation; & to solve for "x" :

2x / 2 = 24 / 2 ;

x = 12 .
__________________________________________________
Method 3).
__________________________________________________
$\frac{2}{3}$ x − 6 = 2 ; Solve for "x" ;
_______________________________________________
Add "6" to EACH SIDE of the equation;
_______________________________________________
→ $\frac{2}{3}$ x − 6 + 6 = 2 + 6 ;

to get:

→ $\frac{2}{3}$ x = 8 ;
______________________________________________
Now, divide each side of the equation by " $\frac{2}{3}$ " ;
to isolate "x" on one side of the equation; & to solve for "x" ;
___________________________________________________
{ $\frac{2}{3}$ x } / { $\frac{2}{3}$ } = 8 / { $\frac{2}{3}$ } ;

to get: x = 8 / { $\frac{2}{3}$ } ;

= 8 * ( $\frac{3}{2}$ ;

= $\frac{8}{1}$ * $\frac{3}{2}$ ;

= $\frac{8*3}{1*2}$ ;

= $\frac{24}{2}$ ;

= 12 ;
___________________________________________
x = 12 .
___________________________________________
NOTE: Variant: (in "Methods 2 & 3") :
___________________________________________
At the point where:
___________________________________________
= 8 * ( $\frac{3}{2}$ ) ;

= $\frac{8}{1}$ * $\frac{3}{2}$ ;
__________________________________________
We can cancel out the "2" to a "1" ; and we can cancel out the "8" to a "4" ;
__________________________________________
{since: "8÷2 = 4" ; and since: "2÷2 =1" } ;
__________________________________________
and we can rewrite the expression:
__________________________________________
$\frac{8}{1}$ * $\frac{3}{2}$ ;
__________________________________________
as: $\frac{4}{1}$ * $\frac{3}{1}$ ;
__________________________________________
which equals:
__________________________________________
→ $\frac{4*3}{1*1}$ ;

= $\frac{12}{1}$ ;

= 12 .
__________________________________________
x = 12 .
__________________________________________
Answer: The number is: " 12 ".
__________________________________________

8 0

4 years ago

12x−5y=−20 y=x+4 x=x=x, equals y=y=y, equals

aksik [14]

Answer:

The solution is (0, 4)

Step-by-step explanation:

Please pay attention to the first two equations and drop the last two:

12x−5y=−20 y=x+4 x=x=x, equals y=y=y should ideally be:

12x−5y=−20

y=x+4

Let's find x. Substitute x + 4 for y in the first equation, obtaining:

12x - 5(x + 4) = -20

Carrying out the indicated multiplication, we get:

12x - 5x - 20 = -20, or 7x = 0

If x = 0 then y must be 0 + 4, or 4.

The solution is (0, 4)

8 0

3 years ago

CAN SOMEONE PLEASE HELP ME ? SO DETERMINE IF THE PRODUCT OF 3 SQAURE ROOT 2 AND 8 SQUARE ROOT 18 IS RATIONAL OR IRRATIONAL. EXPL

Marta_Voda [28]

Oh ok so square root of 2 is irrational since it goes on and on. square root of 18 is an irrational number too

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3 years ago

Complete the table for the given rule y=x-1/4

leonid [27]

Answer:

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3 years ago

Read 2 more answers