Solve the system of equations by the elimination method.
-0.3x + 0.5y = 3.1 x - 0.1y = 1.5
A) (0.2, 0.5)
B) (5, 2)
C) no solution
D) (2, 5)

Question

Quizplus · Accepted Answer

To solve the system of equations by the elimination method, we first align the equations and then manipulate them to eliminate one variable. The given equations are:1) $0.3x + 0.5y = 3.1$2) $x - 0.1y = 1.5$To eliminate $y$, we can multiply the second equation by 5 to make the coefficients of $y$ in both equations equal in magnitude but opposite in sign:$5(x - 0.1y) = 5(1.5)$$5x - 0.5y = 7.5$Now, we have the system:1) $0.3x + 0.5y = 3.1$2) $5x - 0.5y = 7.5$Adding these two equations to eliminate $y$, we get:$0.3x + 5x = 3.1 + 7.5$$5.3x = 10.6$$x = 2$Substitute $x = 2$ into one of the original equations to solve for $y$. Using the second equation:$2 - 0.1y = 1.5$$0.1y = 2 - 1.5$$0.1y = 0.5$$y = 5$Therefore, the solution is $x = 2$, $y = 5$, which corresponds to choice D) (2, 5).

Solve the System of Equations by the Elimination Method