Solve the system of equations using the addition method:
2x + 5y = 19
3x + y = 9
A) $( 4 , - 3 )$
B) $\left( 4 \frac { 1 } { 2 } , 2 \right)$
C) $( - 2,15 )$
D) $( 2,3 )$

Question

Solve the system of equations using the addition method: 
2x + 5y = 19
3x + y = 9
A) $( 4 , - 3 )$
B) $\left( 4 \frac { 1 } { 2 } , 2 \right)$
C) $( - 2,15 )$
D) $( 2,3 )$

Quizplus · Accepted Answer

To solve the system of equations using the addition method, we need to get one variable to have the same coefficient and opposite signs in both equations. In this case, we can multiply the second equation by -5 to get -15x - 5y = -45. We can then add this equation to the first equation and eliminate the y variable:

2x + 5y = 19 
-15x - 5y = -45 
________________ 
-13x = -26

Solving for x, we get x = 2. We can then substitute this value back into one of the original equations to solve for y. Using the second equation, we have:

3x + y = 9 
3(2) + y = 9 
6 + y = 9 
y = 3

Thus, the solution to the system of equations is (2, 3), which corresponds to choice D.

Solve the System of Equations Using the Addition Method (4,−3)( 4 , - 3 )(4,−3)

Solve the System of Equations Using the Addition Method $( 4 , - 3 )$