find the coordinates of the intersection point that solves the system of these two linear eqations in two variabals: 2x + y = 15 and y = -x + 5
A. (-5, 10
B. (10, -5)
C. (5,-10)
D. (-10, 5)
To solve the system of equations, we can use the method of substitution.
First, we solve the second equation for y:
y = -x + 5
Next, we substitute this expression for y in the first equation:
2x + (-x + 5) = 15
Simplifying the equation:
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 substitute it into the second equation:
y = -x + 5
y = -10 + 5
y = -5
Therefore, the intersection point is (10, -5), which corresponds to option B.
To find the coordinates of the intersection point that solves the system of the two linear equations, we need to solve them simultaneously.
The given equations are:
1) 2x + y = 15
2) y = -x + 5
We can substitute equation 2 into equation 1 to eliminate one variable and solve for the other.
Substitute y = -x + 5 into equation 1:
2x + (-x + 5) = 15
Simplify the equation:
2x - x + 5 = 15
x + 5 = 15
x = 15 - 5
x = 10
Substitute the value of x into equation 2 to find the value of y:
y = -x + 5
y = -10 + 5
y = -5
Therefore, the coordinates of the intersection point are (10, -5).
The correct answer is:
B. (10, -5)
To find the coordinates of the intersection point that solves the system of the given linear equations, you need to solve the equations simultaneously by finding the values of x and y that satisfy both equations.
Given equations:
1) 2x + y = 15
2) y = -x + 5
We can solve this system of equations using the method of substitution. In the second equation, you can see that y is already isolated, so we can substitute it into the first equation:
2x + (-x + 5) = 15
Now, simplify:
2x - x + 5 = 15
Combine like terms:
x + 5 = 15
Subtract 5 from both sides:
x = 10
Now that we have the value of x, we can substitute it back into one of the equations (either equation 1 or equation 2) to find the value of y. Let's use equation 2:
y = -x + 5
y = -(10) + 5
y = -10 + 5
y = -5
Therefore, the intersection point that solves the system of equations is (10, -5).
So, the correct answer is:
B. (10, -5)