Question

When the method of substitution is used to solve the system −3x−2y=1 −x+y=3, a possible third equation to be solved is:

a) −3x−2(−x+3)=1
b) 3(x+1)=1
c) −3x−2(x+3)=1
d) 3x−2(x+3)=1

Answer 1

When using the method of substitution to solve the system -3x-2y=1 and -x+y=3, we can express y in terms of x and substitute it into the first equation, resulting in -3x -2(x+3) = 1.

Step-by-step explanation:

When using the method of substitution to solve the system -3x-2y=1 and -x+y=3, we want to express one variable in terms of the other in order to substitute it into the other equation.

In this case, we can express y in terms of x from the second equation: y = x + 3.

Now we can substitute this expression for y into the first equation: -3x - 2(x+3) = 1. Simplifying this equation gives us -3x -2x - 6 = 1, which is option c) -3x -2(x+3) = 1.