Question

$x + y = - 1 \\ 3x - 2y = 22$
​

Answer 1

x + y = -1

y = - 1 - x

y = - (1 + x)

- y = 1 + x ... (i)

3x - 2y = 22

3x + 2(-y) = 22

3x + 2(1 + x) = 22

3x + 2 + 2x = 22

5x + 2 = 22

5x = 20

x = 4

substituting in (i)

- y = 1 + x = 1 + 4 = 5

- y = 5

y = -5

Hence, (x, y) = (4, -5) is the solution of the given pair of linear equations.

Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\underline{\mathfrak{\: Given , \: }} \\ \\ \: \: \: \: \: \tt{x + y = - 1 \: \: - - - - - - > (1)} \\ \\ \: \: \tt{3x - 2 y = 22\: \: - - - - - - > (2)}$

$\sf{(1) \implies \: y = - 1 - x \: \: - - - - - - > (3)}$

$\underline{ \text{ \: \: Putting the value of \: \red{y} \: from eq. (3) in eq. (2), we get, \: \: }}$

$\tt{(2) \implies \: 3x - 2y = 22}\\ \\ \: \: \: \: \: \: \: \tt{\implies \: 3x - 2 \red{( - 1 - x)} = 22} \\ \\ \: \: \: \: \: \: \: \tt{ \implies \:3x + 2 + 2x = 22 } \\ \\ \: \: \: \: \: \: \: \tt{ \implies \: 5x + 2 = 22} \\ \\ \: \: \: \: \: \: \: \tt{ \implies \: 5x = 22 - 2} \\ \\ \: \: \: \: \: \: \: \tt{ \implies \: 5x = 20} \\ \\ \: \: \: \: \: \: \: \tt{ \implies \: x = \frac{20}{5} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ \therefore \: \: \red{ x = 4}}$

$\underline{ \text{ \: \: Putting the value of \: \red{x} \: in eq. (3), we get, \: \: }}$

$\sf{ (3) \implies \: y = - 1 - x} \\ \\ \: \: \: \: \: \: \: \sf{ \implies \: y = - 1 - \red{4}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\sf{ \therefore \: \red{y = - 5}}$

$\huge{ \bold{ \therefore \: \underline{ \red{x = 4} }\: \: \: and \: \: \: \underline{\red{ y = - 5 }}}}$