The lowest grade is 48.
The substitution method is the algebraic method to solve simultaneous linear equations. In this method, the value of one variable from one equation is substituted in the other equation.
Let the lowest grade be x and highest grade be y.
According to the given question.
[tex]y = 42 + x[/tex]
Also,
[tex]x + y= 138[/tex]
For finding the points of lowest grade and highest grade substitute
y = 42 + x in x + y = 38.
[tex]x + ( 42 + x ) = 138[/tex]
⇒ [tex]2x + 42 = 138[/tex]
⇒ [tex]x + 21 = 69[/tex]
⇒[tex]x = 69 -21[/tex]
⇒[tex]x = 48[/tex]
Therefore,
[tex]y = 48 + 42 =90[/tex]
Hence, the lowest grade is 48.
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