Question

Find the value x and y using substitution method: 2x−5y = 9 and 5x+6y = 8.
(a)94 and 199
(b)$\dfrac{94}{37}$ and $\dfrac{-145}{185}$
(c)$\dfrac{-94}{43}$ and $\dfrac{199}{215}$
(d)$\dfrac{-94}{43}$ and $\dfrac{-199}{215}$

Answer 1

Hint: In the substitution method we solve for one variable, and then substitute that expression into the other equation. The important thing here is that we are always substituting values that are equivalent.

Complete step-by-step answer:
Substitution method can be applied in four steps
Step 1: Solve one of the equations for either x or y.
Step 2: Substitute the solution from step 1 into the other equation.
Step 3: Solve this new equation.
Step 4: Solve for the second variable.
Let us consider,
2x-5y = 9……………(1)
5x+6y = 8……………(2)
Solve one of the equations for either x or y. We will solve the first equation for y.
2x-5y = 9
$y=\dfrac{2x-9}{5}$
Substitute the solution from step 1 into the second equation
5x+6y = 8
$5x+6\left( \dfrac{2x-9}{5} \right)=8$
Solve this new equation.
$\begin{align}
  & 25x+12x-54=40 \\
 & 37x=40+54 \\
 & x=\dfrac{94}{37} \\
\end{align}$
Solve for the second variable
$\begin{align}
  & 2\left( \dfrac{94}{37} \right)-5y=9 \\
 & 188-185y=333 \\
 & 188-333=185y \\
 & -145=185y \\
 & y=\dfrac{-145}{185} \\
\end{align}$
Hence the value of $x=\dfrac{94}{37}$ and $y=\dfrac{-145}{185}$ .
Therefore, the correct option for the given question is option (b).

Note: When two equations of a line intersect at a single point, we say that it has a unique solution which can be described as a point, (x, y), in the XY-plane. The substitution method is used to solve systems of linear equations by finding the exact values of x and y which correspond to the point of intersection.