Question

Monday is our deadline, can someone help me?.
$x + y = 10 x - y = 16$
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Answer 1

Answer:

1) y(10-y)=16

10y-y2=16

y2-10y+16=0

y2-8y-2y+16=0

y(y-8)-2(y-8)=0

y-2=0

y=2 and if y=2 then x=8

y-8=0

y=8 then x=2

Explanation:

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Answer 2

Answer:

Answer :

• The value of x is 13.
• The value of y is -3.

Question :

1. Solve each system of equations by substitution check your solution.

$\begin{gathered}\begin{gathered}\small\star \: \sf{\underline{\underline{\red{1.}}}}\begin{cases}\sf{x + y= \bf{10}} \\ \\ \sf{x - y= \bf{16}}\end{cases} \end{gathered}\end{gathered}$

Solution :

Here, we will use the below following steps to find a solution using the transposition method:

• Step 1:- We will Identify the variables and constants in the given simple equation.
• Step 2:- Then we Simplify the equation in LHS and RHS.
• Step 3:- Transpose or shift the term on the other side to solve the equation further simplest.
• Step 4:- Simplify the equation using arithmetic operation as required that is mentioned in rule 1 or rule 2 of linear equations.
• Step 5:- Then the result will be the solution for the given linear equation. By using the transposition method. we get,

$\rule{190}{1}$

Here,

• x + y = 10 • • • • (i)
• x - y = 16 • • • • (ii)

$\rule{190}{1}$

From equation (ii),

$\begin{gathered}\qquad{\implies{\sf{x - y = 16}}} \\ \\ \qquad{\implies{\sf{x = 16 + y}}}\end{gathered}$

$\rule{190}{1}$

Now, putting the value of x is equation (i)

$\begin{gathered}\qquad{\implies{\sf{x + y = 10}}}\\\\\qquad{\implies{\sf{( 16 + y )+ y = 10}}}\\\\\qquad{\implies{\sf{y + y = 10 - 16}}}\\\\\qquad{\implies{\sf{y+ y = 10}}}\\\\\qquad{\implies{\sf{y + y = -6}}}\\\\\qquad{\implies{\sf{2y = -6}}}\\\\\qquad{\implies{\sf{y = \dfrac{ - 6}{2}}}}\\\\\qquad{\implies{\sf{y=\cancel{\dfrac{ - 6}{2}}}}}\\\\\qquad{\implies{\sf{\underline{\underline{\red{y = - 3}}}}}}\end{gathered}$

Hence, the value of y is -3.

$\rule{190}{1}$

Now, putting the value of y in equation (ii):

$\begin{gathered}\qquad{\implies{\sf{x - y = 16}}}\\\\\qquad{\implies{\sf{x - ( - 3) = 16}}}\\\\\qquad{\implies{\sf{x + 3 = 16}}}\\\\\qquad{\implies{\sf{x = 16 - 3}}}\\\\\qquad{\implies{\sf{\underline{\underline{\red{x = 13}}}}}}\end{gathered}$

Hence, the value of x is 13.

$\underline{\rule{220pt}{3pt}}$