Question

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)

Answer 1

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 2

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*2=-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=(25)/(5)\\\\\Rightarrow x=5.`

From equation (iv), we get

`2*5-4y=-6\\\\\Rightarrow 10-4y=-6\\\\\Rightarrow 4y=16\\\\\Rightarrow y=(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).