Question

Solve the system of equations by substitution. What is the solution for x? 2x + y = 1 4x + 2y = −1

a. x = 0
b. x = 2
c. There is no x value as there is no solution.
d. x can be any value as there is an infinite number of solutions.

Answer 1

`2x+y=1 \ \ \ \ \ \ \ \ |* (-2) \\ 4x+2y=-1 \\ \\ -4x-2y=-2 \\ \underline{4x+2y=-1 \ \ \ } \\ 0=-3 \\ false \\ \\ \hbox{no solution}`

The answer is C.

Answer 2

solve your system of equations.

2x+y=1;4x+2y=−1

Solve 2x+y=1 for y:

2x+y+−2x=1+−2x(Add -2x to both sides)

y=−2x+1

Substitute (−2x+1) for y in 4x+2y=−1:

4x+2y=−1

4x+2(−2x+1)=−1

2=−1(Simplify both sides of the equation)

2+−2=−1+−2(Add -2 to both sides)

0=−3

Answer: No solution. C)