Question

What is the value of the x variable in the solution to the following system of equations? 3x + 2y = 8 2x + 3y = 2

a. 4
b. −2
c. x can be any number as there are infinitely many solutions to this system
d. There is no x value as there is no solution to this system

Answer 1

`3x+2y=8 \ \ \ \ \ |* 3 \\ 2x+3y=2 \ \ \ \ \ |* (-2) \\ \\ 9x+6y=24 \\ \underline{-4x-6y=-4} \\ 5x=20 \\ x=(20)/(5) \\ x=4`

The answer is A.

Answer 2

solve your system of equations.

3x+2y=8;2x+3y=2

Solve 3x+2y=8 for x:

3x+2y+−2y=8+−2y(Add -2y to both sides)

3x=−2y+8

3x/3=−2y+83(Divide both sides by 3)

x=−2/3y+8/3

Substitute (−2/3y+8/3) for x in 2x+3y=2:

2x+3y=2

2(−2/3y+8/3)+3y=2

5/3y+16/3=2(Simplify both sides of the equation)

5/3y+16/3+−16/3=2+−16/3(Add (-16)/3 to both sides)

5/3y=−10/3

5/3y5/3=−10/35/3(Divide both sides by 5/3)

y=−2

Substitute (−2) for y in x=−2/3y+8/3:

x=−23y+83

x=−23(−2)+83

x=4(Simplify both sides of the equation)

Answer is A)