Review the graphs of a system of two linear equations in two variables: y=x−6 and y=−x+4 . Find the solution to both equations.
To find the solution to both equations, we can set them equal to each other and solve for the values of x and y:
x - 6 = -x + 4
2x = 10
x = 5
Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y:
y = x - 6
y = 5 - 6
y = -1
Therefore, the solution to the system of equations y=x−6 and y=−x+4 is (5, -1).
Now let's plot the two equations on a graph to visualize their intersection:
Equation 1: y=x-6
Equation 2: y=-x+4
The graph shows that the two lines intersect at the point (5, -1), confirming our solution.