Question

solve the PLE by elimination method x+y=8 and 2x+y=13
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Answer 1

Answer:

The solution to the given problem is:

$x=5 \text { and } y=3$

Step-by-step explanation:

Given: The equations are$x+y=8 \ and\ 2x+y=13$.

We have to solve the above equations by the elimination method.

• As we know, the elimination method is the process of eliminating one of the variables in the system of linear equations using addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.

We are solving in the following way:

We have,

The equations are$x+y=8 \ and\ 2x+y=13$.

Let assume,

$x+y=8\ \ ..1) \\ 2x+y=13\ \ ..2)$

Multiplying the second equation by -1, then adding the equations together we get;

$\begin{array}{l}(x+y=8) \\-1(2 x+y=13)\end{array}$

Becomes:

$\begin{array}{l}x+y=8 \\-2 x-y=-13\end{array}$

Adding these equations to eliminate y:

$-x=-5$

$\begin{array}{l}-x=-5 \\\\\frac{-x}{-1}=\frac{-5}{-1} \ \ (Dividing\ both\ sides \ by -1)\\\\x=5\end{array}$

Hence, we get thenvalue of x is 5.

$\text { Substitute } 5 \text { for } x \text { in } x+y=8 \text { : }$

$5+y=8\\y+5+-5=8+-5 \text { (Adding }-5 \text { to both sides) }\\y=3$

Hence, we get,

$x=5 \text { and } y=3$

Note:

Q.Solve the equations by elimination method x+y=8 and 2x+y=13.