Question

Solve the system of equations using subtraction. y = -2x + 1 4x + 2y = -3 a. Infinity many solutions b. No solution c. (0,-5) d. (-5,0)

Answer 1

Given:

The given system of equation is:

$y=-2x+1$

$4x+2y=-3$

To find:

The solution of given system of equations using subtraction.

Solution:

We have,

$y=-2x+1$             ...(i)

$4x+2y=-3$         ...(ii)

First equation can be rewritten as

$2x+y=1$             (Adding 2x on both sides)

$4x+2y=2$       ...(iii)        (Multiplying both sides by 2)

After subtracting (ii) from (iii), we get

$4x+2y-(4x+2y)=2-(-3)$

$4x+2y-4x-2y=2+3$

$0=5$

This statement is false because $0\neq 5$. It means, there is no value of x and y for which the given system of equations are true.

Therefore, the given system of equations has no solution and the correct option is b.