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Maths-

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Question

$table attributes columnalign right columnspacing 1em end attributes row cell 2 x plus 3 y equals 2 end cell row cell x minus 2 y equals 8 end cell end table$
The solution to the given system of equations is (x, y). What is the value of x?

The correct answer is: x=4 and y = -2

HINT: Eliminate any one variable(suppose x) and find the other variable's value(i.e y) and substitute the value(i.e y) in any equation to find the value of the eliminated variable (i.e x).
Step 1: Eliminating x
$2 x plus 3 y equals 2$ —-(eq 1)
$x minus 2 y equals 8 minus negative cross times 2 not stretchy rightwards double arrow 2 x minus 4 y equals 16$ —(eq 2)
Subtraction eq1 from eq 2 i.e (eq 2 - eq 1)
$negative 7 y equals 14 not stretchy rightwards double arrow y equals negative 2$
Step 2: substitute y = -2 in eq 1 to find x
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 2 x plus 3 y equals 2 end cell row cell 2 x plus 3 left parenthesis negative 2 right parenthesis equals 2 end cell row cell 2 x equals 2 plus 6 end cell row cell x equals 4 end cell end table$
∴ x = 4 and y = -2 ;(x, y) = (4,-2) is the solution to the given system of equation

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