Solve by the elimination method: $$\begin{array} { l }
5 x + 5 y = 30 \
2 x + 2 y = 3
\end{array}$$
A) (5, 1)
B) (-10, 16)
C) (0, 6)
D) (-5, 11)
E) No solution

Question

Solve by the elimination method: $$\begin{array} { l } 
5 x + 5 y = 30 \
2 x + 2 y = 3
\end{array}$$
A) (5, 1)
B) (-10, 16)
C) (0, 6)
D) (-5, 11)
E) No solution

Quizplus · Accepted Answer

To solve the system of equations by the elimination method, we first try to eliminate one of the variables by making the coefficients of that variable the same in both equations. However, in this case, if we attempt to eliminate either $x$ or $y$ by multiplying the equations to get the same coefficients, we end up with an inconsistency.Let's simplify the equations first by dividing them to get their simplest form:1. $5x + 5y = 30$ can be divided by 5 to get $x + y = 6$.2. $2x + 2y = 3$ can be divided by 2 to get $x + y = 1.5$.We now have two equations:$$x + y = 6$$$$x + y = 1.5$$These two equations are contradictory because they assert that the same expression, $x + y$, is equal to two different numbers, 6 and 1.5. This means there is no solution to the system of equations, indicating that the lines represented by these equations are parallel and never intersect.

Solve by the Elimination Method 5x+5y=302x+2y=3\begin{array} { l } 5 x + 5 y = 30 \\2 x + 2 y = 3\end{array}5x+5y=302x+2y=3​

Solve by the Elimination Method $\begin{array} { l } 5 x + 5 y = 30 \\2 x + 2 y = 3\end{array}$