Consider this linear system:
3x − 2y = −2
x + 3y = 14
Question 1
To solve this system by substitution, which expression could be substituted for x?
A. 3y + 143y + 14
B. 3y − 143y − 14
C. −3y + 14−3y + 14
D. −3y − 14
To solve this linear system by substitution, we want to isolate one variable in one equation and substitute it into the other equation.
Let's isolate x in the second equation:
x + 3y = 14
x = 14 - 3y
We can substitute "14 - 3y" for x in the first equation:
3x - 2y = -2
3(14 - 3y) - 2y = -2
42 - 9y - 2y = -2
-11y + 42 = -2
-11y = -2 - 42
-11y = -44
y = (-44)/(-11)
y = 4
Now that we have the value of y, we can substitute it back into the second equation to find x:
x + 3y = 14
x + 3(4) = 14
x + 12 = 14
x = 14 - 12
x = 2
Therefore, the expression that could be substituted for x is:
A. 3y + 14