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 negative 10 comma 5 right parenthesis (−5, 10) left parenthesis negative 5 comma 10 right parenthesis (10,−5) left parenthesis 10 comma negative 5 right parenthesis (5,−10)
To find the intersection point, we need to solve the system of equations:
Equation 1: 2x + y = 15
Equation 2: y = -x + 5
We can substitute Equation 2 into Equation 1 to eliminate y:
2x + (-x + 5) = 15
Combine like terms:
x + 5 = 15
Subtract 5 from both sides:
x = 10
Now, substitute x = 10 into Equation 2 to solve for y:
y = -(10) + 5
y = -5
Therefore, the intersection point is (10, -5).
To find the intersection point, we need to solve the system of equations:
2x + y = 15 ...(Equation 1)
y = -x + 5 ...(Equation 2)
To solve this system, we can substitute the value of y from Equation 2 into Equation 1:
2x + (-x + 5) = 15
Simplifying the equation, we get:
2x - x + 5 = 15
x + 5 = 15
x = 15 - 5
x = 10
Now, substitute the value of x back into Equation 2 to find y:
y = -(10) + 5
y = -10 + 5
y = -5
Therefore, the intersection point is (10, -5).
To find the coordinates of the intersection point that solves the system of linear equations, we need to solve the equations simultaneously.
Let's start by solving the system using the substitution method:
1. Begin with the equation y = -x + 5.
2. Substitute this value of y into the other equation:
2x + (-x + 5) = 15.
3. Simplify the equation by combining like terms:
2x - x + 5 = 15.
x + 5 = 15.
4. Subtract 5 from both sides of the equation:
x + 5 - 5 = 15 - 5.
x = 10.
Now that we have the value of x, we can substitute it back into one of the original equations to find the corresponding y-coordinate:
1. Using the equation y = -x + 5, substitute x = 10:
y = -(10) + 5.
y = -10 + 5.
2. Simplify:
y = -5.
Therefore, the intersection point that solves the system of equations is (10, -5).