All categories

4 years ago

Solve the equations using substitution 7x-2y=3 14x+y=14

Mathematics

1 answer:

Setler79 [48]4 years ago

8 0

Answer:

x = 31/35 , y = 8/5

Step-by-step explanation:

Solve the following system:

{7 x - 2 y = 3

14 x + y = 14

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for y:

{7 x - 2 y = 3

14 x + y = 14

Hint: | Solve for y.

Subtract 14 x from both sides:

{7 x - 2 y = 3

y = 14 - 14 x

Hint: | Perform a substitution.

Substitute y = 14 - 14 x into the first equation:

{7 x - 2 (14 - 14 x) = 3

y = 14 - 14 x

Hint: | Expand the left hand side of the equation 7 x - 2 (14 - 14 x) = 3.

7 x - 2 (14 - 14 x) = (28 x - 28) + 7 x = 35 x - 28:

{35 x - 28 = 3

y = 14 - 14 x

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for x:

{35 x - 28 = 3

y = 14 - 14 x

Hint: | Isolate terms with x to the left hand side.

Add 28 to both sides:

{35 x = 31

y = 14 - 14 x

Hint: | Solve for x.

Divide both sides by 35:

{x = 31/35

y = 14 - 14 x

Hint: | Perform a back substitution.

Substitute x = 31/35 into the second equation:

Answer: {x = 31/35 , y = 8/5

You might be interested in

At maximum speed, an airplane tracked 1720 miles against the wind in 5 hours. Flying with the wind, the plane can travel the sam

nataly862011 [7]

Recall your d = rt, distance = rate * time.

as the plane goes against the wind, the plane is not really flying at "x" mph, but is really going slower, at " x - y ", because the wind is subtracting speed from it.

likewise, when the plane is going with the wind, is not really going at "x" mph, but at " x + y ", is going faster due to the wind, thus

$\bf \begin{array}{lccclll}
&\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\
&------&------&------\\
\textit{against the wind}&1720&x-y&5\\
\textit{with the wind}&1720&x+y&4
\end{array}
\\\\\\
\begin{cases}
1720=(x-y)5\implies \frac{1720}{5}=x-y\\\\
344=x-y\implies \boxed{y}=x-344\\
---------------\\
1720=(x+y)4\implies \frac{1720}{4}=x+y\\\\
430=x+y\implies 430=x+\left( \boxed{x-344} \right)
\end{cases}
\\\\\\
430=2x-344\implies 774=2x\implies \cfrac{774}{2}=x\implies 387=x$

6 0

3 years ago

How much does cell phone weigh

noname [10]

In 2005 he average weight is 4 ounces, they have gotten bigger since, clearly, but that is the average weight.
Does this answer your question?<span />

5 0

3 years ago

Read 2 more answers

The following formula models the number of prison inmates, P, in thousands, who are in U.S prisons x years after 1980.

MariettaO [177]

2X^2+22x+318=1270
2x^2+22x-952=0
x^2+11x-476=0
(x+28)(x-17)=0
x=17

7 0

3 years ago

Which point is the incenter of the triangle?

Likurg_2 [28]

The answer is A for this problem

6 0