Final answer:
To find the sum of the first equation and three times the second equation, the second equation is multiplied by 3 and added to the first one. Like terms are combined to yield the final result, 14x = -14, where the y terms cancel each other out.
Step-by-step explanation:
To write an equation that is the sum of the first equation and three times the second equation, we need to multiply the entire second equation by 3 and add it to the first equation. Let's go through this step by step:
First equation: 2x – 3y = 7
Second equation: 4x + y = -7
Multiply the second equation by 3: 3(4x + y) = 3(-7), which simplifies to 12x + 3y = -21.
Add this result to the first equation: (2x – 3y) + (12x + 3y) = 7 + (-21).
Simplify by combining like terms: 2x + 12x = 14x and – 3y + 3y = 0y, so y's term will cancel out.
The final equation by adding both sides: 14x = -14
There you have the equation based on the sum of the first equation and three times the second equation, with like terms combined.