Use the substitution method to solve the following system: $$\left\{ \begin{array} { l }
2 x = \frac { 1 } { 2 } y - 1.2 \
\frac { 1 } { 5 } y = 6 x - 1.6
\end{array} \right.$$
A)(-1.6, 4)
B)(0.4, 4)
C)(0.5, 3)
D)The equations are dependent.
E)The system is inconsistent.

Question

Use the substitution method to solve the following system: $$\left\{ \begin{array} { l } 
2 x = \frac { 1 } { 2 } y - 1.2 \
\frac { 1 } { 5 } y = 6 x - 1.6
\end{array} \right.$$
A)(-1.6, 4)
B)(0.4, 4)
C)(0.5, 3)
D)The equations are dependent.
E)The system is inconsistent.

Quizplus · Accepted Answer

To solve the system using substitution, we first express one variable in terms of the other from one equation and then substitute it into the second equation. From the first equation, we can express $y$ in terms of $x$: $$2x = \frac{1}{2}y - 1.2$$ Multiplying both sides by 2 to get rid of the fraction, we get: $$4x = y - 2.4$$ or $$y = 4x + 2.4$$ Now, substitute $y$ in the second equation: $$\frac{1}{5}y = 6x - 1.6$$ Substituting $y = 4x + 2.4$ into this equation gives: $$\frac{1}{5}(4x + 2.4) = 6x - 1.6$$ Simplifying, we get: $$0.8x + 0.48 = 6x - 1.6$$ Bringing terms involving $x$ to one side and constants to the other side, we get: $$0.8x - 6x = -1.6 - 0.48$$ Simplifying further: $$-5.2x = -2.08$$ Dividing both sides by -5.2 gives: $$x = \frac{-2.08}{-5.2} = 0.4$$ Substituting $x = 0.4$ back into $y = 4x + 2.4$ gives: $$y = 4(0.4) + 2.4 = 1.6 + 2.4 = 4$$ Therefore, the solution to the system is $x = 0.4$ and $y = 4$, which corresponds to choice (B).

Use the Substitution Method to Solve the Following System {2x=12y−1.215y=6x−1.6\left\{ \begin{array} { l } 2 x = \frac { 1 } { 2 } y - 1.2 \\\frac { 1 } { 5 } y = 6 x - 1.6\end{array} \right.{2x=21​y−1.251​y=6x−1.6​

Use the Substitution Method to Solve the Following System $\left\{ \begin{array} { l } 2 x = \frac { 1 } { 2 } y - 1.2 \\\frac { 1 } { 5 } y = 6 x - 1.6\end{array} \right.$