The system of equations can be solved using linear combination to eliminate one of the variables. 2x − y = −4→10x − 5y = −20 3x 5y = 59→3x 5y = 59 13x = 39 which equation can replace 3x 5y = 59 in the original system and still produce the same solution? 2x – y = –4 10x – 5y = –20 7x = 39 13x = 39
Answer:
Option D is correct.
13x = 39
Step-by-step explanation:
The system of equation is given:
\(2x-y = -4\) ....[1]
\(3x+5y = 59\) .....[2]
Multiply equation [1] by 5 to both sides we have;
\(10x-5y = -20\) .....[3]
Using elimination method:
Add [2] and [3] equations to eliminate y and solve for x, we have;
\(13x = 39\)
Divide both sides by 13 we get;
x = 3
Substitute x in [1] we have;
2(3)-y = -4
6-y = -4
Subtract 6 from both sides we have;
-y = -10
Divide both sides by -1 we have;
y = 10
⇒Solution: (3, 10)
Therefore, an equation can replace 3x+5y = 59 in the original system and still produce the same solution is,
13x = 39