Question

Examine this system of linear equations.

y – x = 2,

x + y = 4

Which is a solution of the system of equations?
(1, 3)
(2, 2)
(3, 1)
(4, 2)

Answer 1

Given :

•Examine this system of linear equations :

$\bf \: y - x = 2 \: \: \: \: \: \: .....(1) \\ \bf \: x + y = 4 \: \: \: \: \: \: \: .......(2)$

To find :

•Which is a solution of the system of equations =?

Solution :

$\implies \sf \: y - x = 2 \\ \\ \implies \sf \: - x + y = 2 \\ \\ \implies \boxed{ \sf{ \: x - y = - 2.}}...(1)$

$\implies \boxed{ \sf{ \: x + y =4}}....(2)$

Adding both equations (1) and (2) we get,

$\implies \sf \: \: \: x - \cancel y = - 2 \\ \\ \implies \sf \: x + \cancel y = 4$

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$\implies \sf \: 2x = - 2 + 4 \\ \\ \implies \sf \: 2x = 2 \\ \\ \implies \boxed{ \sf{x = 1}}$

• Put the x value in equation (1) to get y values :

$\implies \sf \: y - x = 2 \\ \\ \implies \sf \: y - 1 = 2 \\ \\ \implies \sf \: y - 1 - 2 = 0 \\ \\ \implies \sf \: y - 3 = 0 \\ \\ \implies \boxed{ \sf{y = 3}}$

•The solution of this equation is (1,3)