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Answered

  1. Solve the system of equations by substitution.

X= -4y

X+5y=2

A(-8,2)
B(8,-2)
C(2/9,-8/9)
D(-12,3)


  1. Solve the system of equations by elimination.

3x+4y=31

2x-4y=-6

A(4,5)
B(5,4)
C(-5,12.5)
D(5,-4)

Verified Answer :

thuytien1501200
  1. plug in x=-4y to the second one (x+5y=2), we have: -4y+5y=2 => y=2. Then plug y=2 to x=-4y we have x=-4(-2)=8. So the answer will be A: (8,-2)

    4. For this one, you add the first equation to the second one, 3x plus 2x = 5x, 4x plus -4x = 0, 31 plus -6= 25. Then we get the final equation is : 5x=25, solve for x we get x=5, plug x=5 to any equation, we get y= 4. So the answer will be B (5,4)

Answer:  The correct options are

(A) (-8, 2)  and  (B) (5, 4).

Step-by-step explanation:  

(1)  We are given to solve the following system of equations by substitution :

\(x=-4y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+5y=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\)

Substituting the value of x from equation (i) in equation (ii), we get

\(x+4y=2\\\\\Rightarrow -4y+5y=2\\\\\Rightarrow y=2.\)

From equation (i), we get

\(x=-4\times2=-8.\)

So, the required solution is (-8, 2).

Option (A) is CORRECT.

(2) We are given to solve the following system of equations by elimination :

\(3x+4y=31~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)\\\\2x-4y=-6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)\)

Adding equations (iii) and (iv), we get

\((3x+4y)+(2x-4y)=31+(-6)\\\\\Rightarrow 5x=25\\\\\Rightarrow x=\dfrac{25}{5}\\\\\Rightarrow x=5.\)

From equation (iv), we get

\(2\times5-4y=-6\\\\\Rightarrow 10-4y=-6\\\\\Rightarrow 4y=16\\\\\Rightarrow y=\dfrac{16}{4}\\\\\Rightarrow y=4.\)

So, the required solution is (5, 4).

Option (B) is CORRECT.

Thus, the correct options are

(A) (-8, 2)  and  (B) (5, 4).

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