For the following system, if you isolated x in the first equation to use the Substitution Method, what expression would you substitute into the second equation?
−x − 2y = −4
3x + y = 12
−2y − 4
2y − 4
2y + 4
−2y + 4 --- I think it'd be this one, is it correct?
To isolate x in the first equation, you need to move the -2y term to the other side of the equation:
−x = -2y - 4
To solve for x, you can multiply both sides of the equation by -1:
x = 2y + 4
When using the Substitution Method, you substitute this expression for x into the second equation, which is:
3x + y = 12
Replacing x with 2y + 4, the equation becomes:
3(2y + 4) + y = 12
Simplifying this equation gives:
6y + 12 + y = 12
Combining like terms:
7y + 12 = 12
So, the expression you should substitute into the second equation is:
2y + 4
To use the Substitution Method, we need to isolate one variable in one equation and substitute its expression into the other equation. In this case, we can isolate "x" in the first equation:
−x − 2y = −4
To isolate "x", we can add "x" to both sides of the equation:
−x + x − 2y = x − 4
-2y = x - 4
Next, we can rewrite it as:
x = 2y + 4
Now, we can substitute the expression "2y + 4" for "x" in the second equation:
3x + y = 12
Substituting, we get:
3(2y + 4) + y = 12
Expanding and simplifying:
6y + 12 + y = 12
7y + 12 = 12
So the correct expression to substitute into the second equation is:
2y + 4