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
(5,−10)
left parenthesis 5 comma negative 10 right parenthesis
(10,−5)
left parenthesis 10 comma negative 5 right parenthesis
To find the intersection point, we can substitute the value of 'y' from the second equation into the first equation.
y = -x + 5
Substituting this value into the first equation:
2x + (-x + 5) = 15
Simplifying the equation:
2x - x + 5 = 15
x + 5 = 15
x = 15 - 5
x = 10
Now, substitute this value of 'x' into the second equation to find 'y':
y = -x + 5
y = -(10) + 5
y = -10 + 5
y = -5
Therefore, the intersection point is (10, -5).
To find the intersection point of the system of equations, we can substitute the value of y from the second equation into the first equation.
Given equations:
1) 2x + y = 15
2) y = -x + 5
Substituting y = -x + 5 into equation (1):
2x + (-x + 5) = 15
Simplifying the equation:
2x - x + 5 = 15
x + 5 = 15
x = 15 - 5
x = 10
Now, substitute the value of x back into the second equation to find 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 intersection point of the system of equations 2x+y=15 and y=-x+5, we need to solve the equations simultaneously. There are multiple ways to do this, but one common method is substitution.
Let's start by substituting the value of y from the second equation into the first equation:
2x + (-x+5) = 15
Simplifying this equation gives us:
2x - x + 5 = 15
x + 5 = 15
x = 15 - 5
x = 10
Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. Let's use the second equation:
y = -x + 5
y = -(10) + 5
y = -10 + 5
y = -5
Therefore, the intersection point of the two equations is (10, -5).