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$-2x+by=59$ $\newline$ $5x-y=1$ $\newline$ If the system of equations has exactly one solution $(x,y)$ and $x=2$ , what is the value of $b$ ?

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Write and solve direct variation equations

Full solution

Q.

-2x+by=59

\newline

5x-y=1

\newline

If the system of equations has exactly one solution

(x,y)

and

x=2

, what is the value of

b

?

Substitute $x$ into second equation: Substitute the given value of $x$ into the second equation. $\newline$ The second equation is $5x - y = 1$ . $\newline$ Substitute $x = 2$ into this equation. $\newline$ $5(2) - y = 1$ $\newline$ $10 - y = 1$
Solve for y in second equation: Solve for y in the second equation. $\newline$ Add $y$ to both sides and subtract $1$ from both sides to isolate $y$ . $\newline$ $10 - y + y = 1 + y$ $\newline$ $10 = y + 1$ $\newline$ Subtract $1$ from both sides. $\newline$ $10 - 1 = y$ $\newline$ $9 = y$
Substitute $x$ and $y$ into first equation: Substitute the values of $x$ and $y$ into the first equation. $\newline$ The first equation is $-2x + by = 59$ . $\newline$ Substitute $x = 2$ and $y = 9$ into this equation. $\newline$ $-2(2) + b(9) = 59$ $\newline$ $-4 + 9b = 59$
Solve for b in first equation: Solve for b in the first equation. $\newline$ Add $4$ to both sides to isolate the term with $b$ . $\newline$ $-4 + 4 + 9b = 59 + 4$ $\newline$ $9b = 63$ $\newline$ Divide both sides by $9$ to solve for $b$ . $\newline$ $\frac{9b}{9} = \frac{63}{9}$ $\newline$ $b = 7$

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