Choose the equivalent system of linear equations that will produce the same solution as the one given below.
4x - 2y = 6
2x + y = 5
Options:
A) -4x - 2y = 10
-4y = 4
B) -4x - 5y = -1
-7y = 5
C) 3x + 2y = 6
7x = 12
D) 4x + 2y = 10
8x = 16
<h3><u>Answer:</u></h3>Option D
The equivalent system of linear equations that will produce the same solution as the one given is 4x + 2y = 10 and 8x = 16
<h3><u>Solution:</u></h3>Given system of equations are:
4x - 2y = 6 --------- eqn 1
2x + y = 5 ------- eqn 2
Multiply eqn 2 by 2
2(2x + y = 5)
4x + 2y = 10 --------- eqn 3
Add eqn 1 and eqn 3
4x - 2y + 4x + 2y = 6 + 10
8x = 16
x = 2
Substitute x = 2 in eqn 1
4(2) - 2y = 6
8 - 2y = 6
2y = 8 - 6
2y = 2
y = 1
Thus the solution of given system of equations is (x , y) = (2, 1)
<h3>Let us check the options one by one</h3><h3>Option A) </h3>Given system of equations are:
-4x - 2y = 10 ---- eqn 1
-4y = 4 --- eqn 2
Substitute the obtained solution (x, y) = (2, 1) in above equations and check if it makes the equation true
From eqn 2,
-4(1) = 4
Thus this option does not produce the same solution as the one given
<h3>Option B)</h3>-4x - 5y = -1 ----- eqn 1
-7y = 5 ------- eqn 2
Substitute the obtained solution (x, y) = (2, 1) in above equations and check if it makes the equation true
From eqn 2,
Thus this option does not produce the same solution as the one given
<h3>Option C)</h3>3x + 2y = 6 ------ eqn 1
7x = 12 --------- eqn 2
Substitute the obtained solution (x, y) = (2, 1) in above equations and check if it makes the equation true
From eqn 2,
Thus this option does not produce the same solution as the one given
<h3>Option D)</h3>4x + 2y = 10 ------ eqn 1
8x = 16 -------- eqn 2
Substitute the obtained solution (x, y) = (2, 1) in above equations and check if it makes the equation true
From eqn 2,
8(2) = 16
16 = 16
Also,
from eqn 2,
8x = 16
x = 2
substitute x = 2 in eqn 1
4(2) + 2y = 10
8 + 2y = 10
2y = 2
y = 1
Thus solution is (2, 1)
Thus this option produce the same solution as the one given