Question - Solving Equations by Addition
Solution:
To solve the given equations by addition, you'll combine like terms from each equation. Here are the equations:-2x + 4y = 15-12x - 4y = -8When you add them together, the terms -2x and -12x combine to make -14x, and the terms 4y and -4y cancel each other out, leaving 0y (which is simply 0). The right side of the equations will be added as well: 15 + (-8).So the sum of the two equations is:-14x + 0 = 15 - 8Simplify the right side:-14x = 7Now, to solve for x, you need to isolate x by dividing by the coefficient -14:x = 7 / (-14)Simplifying this fraction:x = -1/2The value that belongs in the green box is not the value for x but rather the calculated right side of the equation, which is 7. Therefore, the answer to what value belongs in the green box is not directly given by the simplified form of x, but rather by the combined terms on the right side before we divide by -14. So the answer is 7, which corresponds to option B.
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