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3. 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)


4. 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)

Respuesta :

thuytien1501200
3. 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 :

[tex]x=-4y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+5y=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

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

[tex]x+4y=2\\\\\Rightarrow -4y+5y=2\\\\\Rightarrow y=2.[/tex]

From equation (i), we get

[tex]x=-4\times2=-8.[/tex]

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

Option (A) is CORRECT.

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

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

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

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

From equation (iv), we get

[tex]2\times5-4y=-6\\\\\Rightarrow 10-4y=-6\\\\\Rightarrow 4y=16\\\\\Rightarrow y=\dfrac{16}{4}\\\\\Rightarrow y=4.[/tex]

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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