Find the coordinates of the intersection point that solves the system of these two linear equations in two variables: 2x+y=15 and y=−x+5 . (1 point) Responses (10,−5) left parenthesis 10 comma negative 5 right parenthesis (−5, 10) left parenthesis negative 5 comma 10 right parenthesis (−10, 5) left parenthesis negative 10 comma 5 right parenthesis (5,−10)
To solve this system of equations, we can substitute the value of y from the second equation into the first equation:
2x + (-x+5) = 15
Simplifying the equation by combining like terms, we get:
x + 5 = 15
Subtracting 5 from both sides of the equation, we have:
x = 10
Now we can substitute this value of x back into the second equation to find the value of y:
y = -x + 5
y = -10 + 5
y = -5
Therefore, the coordinates of the intersection point are (10, -5).
To find the intersection point of the two linear equations, we need to solve the system of equations simultaneously.
Given the system of equations:
1) 2x + y = 15
2) y = -x + 5
We can substitute equation 2 into equation 1 to solve for x:
2x + (-x + 5) = 15
2x - x + 5 = 15
x + 5 = 15
x = 15 - 5
x = 10
Now, substitute the value of x into equation 2 to solve for y:
y = -x + 5
y = -(10) + 5
y = -10 + 5
y = -5
Therefore, the coordinates of the intersection point are (10, -5).
To find the coordinates of the intersection point that solves the system of linear equations, you can use the method of substitution or elimination.
Let's use the method of substitution:
1. Start with the given equations:
Equation 1: 2x + y = 15
Equation 2: y = -x + 5
2. Substitute Equation 2 into Equation 1, by replacing y with its value from Equation 2:
2x + (-x + 5) = 15
3. Simplify and solve for x:
2x - x + 5 = 15
x + 5 = 15
x = 15 - 5
x = 10
4. Substitute the value of x (10) back into Equation 2 to find y:
y = -x + 5
y = -(10) + 5
y = -10 + 5
y = -5
Therefore, the intersection point that satisfies both equations is (10, -5).
So, the correct answer is: (10, -5).