Question

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.

Answer 1

To find the intersection point of the two equations, we can substitute the value of y from the second equation into the first equation.

Substituting y = -x + 5 into the first equation, we get:

2x + (-x + 5) = 15

Simplifying the equation, we have:

2x - x + 5 = 15
x + 5 = 15

Subtracting 5 from both sides, we have:

x = 15 - 5
x = 10

Now, substitute the 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).