Question

19x-17y=55
17x-19y=53
Solve by using elimination method

Answer 1

Answer:

The solution to the given equations is:

$x=2 \text { and } y=-1$

Step-by-step explanation:

Given: $19x-17y=55;\ 17x-19y=53$

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,

$19x-17y=55;\ 17x-19y=53$

Let assume,

$19x-17y=55\ \ ....1)\\\ 17x-19y=53\ \ ....2)$

Multiplying the first equation by 19, and the second equation by -17.

$\begin{array}{l}19(19 x-17 y=55) \\-17(17 x-19 y=53)\end{array}$

Becomes:

$\begin{array}{l}361 x-323 y=1045 \\-289 x+323 y=-901\end{array}$

Adding these equations to eliminate y:

$72 x=144\\\\x=\frac{144}{72} \\\\x=2$

Hence, we get the value of x is 2.

$\text { Substituting } 2 \text { for } x \text { in } 19 x-17 y=55 \text { : }$

$(19)(2)-17 y=55\\-17 y+38=55$

Adding -38 to both sides:

$-17 y+38+-38=55+-38$

$\begin{array}{l}-17 y=17 \\\\\frac{-17 y}{-17}=\frac{17}{-17} \ \ ...(Dividing\ both\ sides \ by -17)\\\\y=-1\end{array}$

Hence, we get;

$x=2 \text { and } y=-1$