Question

By elimination method
5x+3y=7
7x-9y=8

Answer 1

Answer:-

The Required Values of x and y are $\bf\dfrac{29}{22}$ and $\bf\dfrac{3}{22}$ respectively.

Explanation:-

Given Equations:-

$\\ \tt\mapsto 5x + 3y = 7...eq(1) \\ \\ \tt\mapsto 7x - 9y = 8...eq(2)$

To Find:-

• The solutions of the given equations.

Solution:-

By Multiplying eq(1) by 3:-

$\\ \tt\mapsto3(5x + 3y = 7).$

$\\ \bf= 15x + 9y = 21...eq(3)$

By Adding eq(2) and eq(3) we get:-

$\\ \tt\mapsto(15x + 9y) + (7x - 9y) = 21 + 8.$

$\\ \tt\mapsto15x + 9y + 7x - 9y = 29.$

$\\ \tt\mapsto22x = 29.$

$\\ \large\bf\mapsto \boxed{ \bf x = \frac{29}{22} .}$

By Putting The Value of x in eq(1) we get:-

$\\ \tt\mapsto5 \bigg( \frac{29}{22} \bigg) + 3y = 7.$

$\\ \tt\mapsto \frac{145}{22} + 3y = 7.$

$\\ \tt\mapsto \frac{145 + 66y}{22} = 7.$

$\\ \tt\mapsto145 + 66y = 154.$

$\\ \tt\mapsto66y = 154 - 145.$

$\\ \tt\mapsto66y = 9$

$\\ \tt\mapsto y = \frac{ \cancel9}{ \cancel{66}}.$

$\\ \large\mapsto \boxed{ \bf y = \frac{3}{22}.}$

Therefore The Required Values Of x and y are $\bf\dfrac{29}{22}$ and $\bf\dfrac{3}{22}$ respectively.

Answer 2

Answer:-

Explanation:-

Given Equations:-

$\\ \tt\mapsto 5x + 3y = 7...eq(1) \\ \\ \tt\mapsto 7x - 9y = 8...eq(2)$

To Find:-

The solutions of the given equations.

Solution:-

By Multiplying eq(1) by 3:-

$\\ \tt\mapsto3(5x + 3y = 7).$

$\\ \bf= 15x + 9y = 21...eq(3)$

By Adding eq(2) and eq(3) we get:-

$\\ \tt\mapsto(15x + 9y) + (7x - 9y) = 21 + 8.$

$\\ \tt\mapsto15x + 9y + 7x - 9y = 29.$

$\\ \tt\mapsto22x = 29.$

$\\ \large\bf\mapsto \boxed{ \bf x = \frac{29}{22} .}$

By Putting The Value of x in eq(1) we get:-

$\\ \tt\mapsto5 \bigg( \frac{29}{22} \bigg) + 3y = 7.$

$\\ \tt\mapsto \frac{145}{22} + 3y = 7.$

$\\ \tt\mapsto \frac{145 + 66y}{22} = 7.$

$\\ \tt\mapsto145 + 66y = 154.$

$\\ \tt\mapsto66y = 154 - 145.$

$\\ \tt\mapsto66y = 9$

$\\ \tt\mapsto y = \frac{ \cancel9}{ \cancel{66}}.$

$\\ \large\mapsto \boxed{ \bf y = \frac{3}{22}.}$

Therefore The Required Values Of x and y are $\bf\dfrac{29}{22}$ and $\bf\dfrac{3}{22}$ respectively.

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