Question
What are the coordinates of both 2x+y=15 and y=-x+5
Answers
GPT 3.5
To find the coordinates of the points that satisfy both equations, we need to solve them simultaneously.
First, let's solve the equation 2x + y = 15.
Rearranging the equation, we get y = -2x + 15.
Now, let's substitute this expression for y in the second equation y = -x + 5.
So, -2x + 15 = -x + 5.
Adding x to both sides, we have -x - 2x + 15 = -x + x + 5, which simplifies to -3x + 15 = 5.
Subtracting 15 from both sides, we get -3x = 5 - 15, which simplifies to -3x = -10.
Now, dividing both sides by -3, we have x = -10 / -3, which simplifies to x = 10 / 3 or x = 3.33 (rounded to two decimal places).
Substituting this value of x back into any of the original equations, we can find the corresponding value of y.
Using the equation y = -x + 5, we have y = -3.33 + 5, which simplifies to y = 1.67.
Therefore, the coordinates of the point that satisfies both equations are (3.33, 1.67) or (approximately) (3.33, 1.67).
First, let's solve the equation 2x + y = 15.
Rearranging the equation, we get y = -2x + 15.
Now, let's substitute this expression for y in the second equation y = -x + 5.
So, -2x + 15 = -x + 5.
Adding x to both sides, we have -x - 2x + 15 = -x + x + 5, which simplifies to -3x + 15 = 5.
Subtracting 15 from both sides, we get -3x = 5 - 15, which simplifies to -3x = -10.
Now, dividing both sides by -3, we have x = -10 / -3, which simplifies to x = 10 / 3 or x = 3.33 (rounded to two decimal places).
Substituting this value of x back into any of the original equations, we can find the corresponding value of y.
Using the equation y = -x + 5, we have y = -3.33 + 5, which simplifies to y = 1.67.
Therefore, the coordinates of the point that satisfies both equations are (3.33, 1.67) or (approximately) (3.33, 1.67).