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y=-x+ 5 x 10- -9- -8- -7- -6- -4- -3- -2- 1. -0- -5 -4 -3 -2 -1,0 -1- O (-5, 10) O (5,-10) O (10,-5) O (-10, 5) -2- -3- -4- -5- -6+ -7+ -8- -9- -10 2x + y = 15 1 2 3 4 jo 7 8 9 10 11 12 13 14 15 x 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)
To find the intersection point of the two linear equations, we can solve the system of equations by substitution or elimination. Let's use substitution.
First, we'll solve the second equation, y = -x + 5, for y:
y = -x + 5
Next, we'll substitute this value of y into the first equation, 2x + y = 15:
2x + (-x + 5) = 15
Simplifying the equation, we get:
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 the second equation to find y:
y = -x + 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 these two linear equations, we need to solve the equations simultaneously.
Equation 1: 2x + y = 15
Equation 2: y = -x + 5
We can substitute Equation 2 into Equation 1 to eliminate the variable "y":
2x + (-x + 5) = 15
2x - x + 5 = 15
x + 5 = 15
x = 15 - 5
x = 10
To find the value of "y," substitute the value of "x" into either Equation 1 or 2:
Equation 1: 2x + y = 15
2(10) + y = 15
20 + y = 15
y = 15 - 20
y = -5
Therefore, the coordinates of the intersection point that solves the system of these two linear equations are (10, -5).
To find the coordinates of the intersection point that solves the system of these two linear equations in two variables, we need to solve the system of equations.
First, let's rewrite the equations in the standard form:
2x + y = 15 ---> Equation 1
y = -x + 5 ---> Equation 2
To solve this system of equations, we have a few methods to choose from: substitution, elimination, or graphing. Let's use the substitution method:
Step 1: Solve Equation 2 for y:
y = -x + 5
Step 2: Substitute the value of y from Equation 2 into Equation 1:
2x + (-x + 5) = 15
Step 3: Simplify the equation:
2x - x + 5 = 15
x + 5 = 15
Step 4: Solve for x:
x = 10
Step 5: Substitute the value of x back into Equation 2 to find y:
y = -x + 5
y = -(10) + 5
y = -10 + 5
y = -5
Therefore, the coordinates of the intersection point that solves the system of these two linear equations are (10, -5).