Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
-$$\frac { x } { 3 } + \frac { y } { 3 } = 2$$
$\mathrm { x } - \mathrm { y } = 4$
A) $\{ ( 5,1 ) \}$
B) $\{ ( 4,2 ) \}$
C) $\{ ( x , y ) \mid x - y = 4 \}$
D) $\varnothing$

Question

Quizplus · Accepted Answer

To solve the system, we can multiply the first equation by 3 to eliminate the fractions: $x + y = 6$. Then, using the second equation $x - y = 4$, we can add these two equations together to eliminate $y$: $2x = 10$, so $x = 5$. Substituting $x = 5$ into one of the original equations to solve for $y$, we use $5 - y = 4$, which gives $y = 1$. Therefore, the solution is $(5, 1)$.

Solve the System by the Method of Your Choice x3+y3=2\frac { x } { 3 } + \frac { y } { 3 } = 23x​+3y​=2

Solve the System by the Method of Your Choice $\frac { x } { 3 } + \frac { y } { 3 } = 2$