Find the value of y for which the equation below is true.
|2x| |y + 7|
|x | = |7 - 3y|
3, -3, 1, or 4
Multiply the second equation by 2 to get the system:
|2x| |y + 7|
|2x| = |14 - 6y|
Equating the right-hand side gives us the TWO equations:
2*(7-3*x)=(x+7)
which can be solved for x, and x=1
or
2*(7-3*x)=-(x+7) which gives x=21/5.
Make an appropriate choice of the solutions.
These are matrices.
I get y=1
To find the value of y for which the equation is true, we need to solve the equation. Let's break it down step by step.
First, let's remove the absolute value signs by considering both the positive and negative cases:
Case 1: When 2x and y + 7 are positive:
We can rewrite the equation as:
2x = y + 7
Case 2: When 2x is positive and y + 7 is negative:
We can rewrite the equation as:
2x = -(y + 7)
2x = -y - 7
Case 3: When 2x is negative and y + 7 is positive:
We can rewrite the equation as:
-2x = y + 7
Case 4: When 2x and y + 7 are negative:
We can rewrite the equation as:
-2x = -(y + 7)
-2x = -y - 7
Now we can simplify each case.
Case 1:
2x = y + 7
2(3) = y + 7
6 = y + 7
y = 6 - 7
y = -1
Case 2:
2x = -y - 7
2(3) = -y - 7
6 = -y - 7
y = 6 + 7
y = 13
Case 3:
-2x = y + 7
-2(3) = y + 7
-6 = y + 7
y = -6 - 7
y = -13
Case 4:
-2x = -y - 7
-2(3) = -y - 7
-6 = -y - 7
y = -6 + 7
y = 1
Now we have four possible values for y: -1, 13, -13, and 1.
Out of these values, the only one that is given in the options is 1, so the answer is y = 1.