Solve the system of equations by substitution, if a solution exists.
-$$\left\{ \begin{array} { l }
3 x + 5 y = 5 \
9 x = 10 + 15 y
\end{array} \right.$$
A) $x = \frac { 25 } { 18 } , y = \frac { 1 } { 6 }$
B) $x = \frac { 1 } { 18 } , y = \frac { 1 } { 6 }$
C) Many solutions
D) No solution

Question

Solve the system of equations by substitution, if a solution exists.
-$$\left\{ \begin{array} { l } 
3 x + 5 y = 5 \
9 x = 10 + 15 y
\end{array} \right.$$
A) $x = \frac { 25 } { 18 } , y = \frac { 1 } { 6 }$
B) $x = \frac { 1 } { 18 } , y = \frac { 1 } { 6 }$
C) Many solutions
D) No solution

Quizplus · Accepted Answer

First, solve the first equation for $x$: $3x = 5 - 5y$, so $x = \frac{5 - 5y}{3}$. Substitute this expression for $x$ in the second equation: $9(\frac{5 - 5y}{3}) = 10 + 15y$. Simplify and solve for $y$, you get $y = \frac{1}{6}$. Substitute $y = \frac{1}{6}$ back into any of the original equations to solve for $x$, resulting in $x = \frac{25}{18}$.

Solve the System of Equations by Substitution, If a Solution {3x+5y=59x=10+15y\left\{ \begin{array} { l } 3 x + 5 y = 5 \\9 x = 10 + 15 y\end{array} \right.{3x+5y=59x=10+15y​

Solve the System of Equations by Substitution, If a Solution $\left\{ \begin{array} { l } 3 x + 5 y = 5 \\9 x = 10 + 15 y\end{array} \right.$