The coordinates of (−6, 4) satisfy the equation y = 1/3 x + 6 because (−6, 4) ____.
If (−6, 4) satisfies the equations of two lines, (−6, 4) is ____, so the lines _____ at (−6, 4).
This means that if two lines _____ at (−6, 4), then (−6, 4) is the _____ to the system of equations.
This means that if you substitute −6 for x and 4 for y in the equations, both equations will be ____.
The coordinates of (−6, 4) satisfy the equation (y = frac{1}{3}x + 6) because (−6, 4) is a solution to the equation.
If (−6, 4) satisfies the equations of two lines, (−6, 4) is the point of intersection, so the lines intersect at (−6, 4).
This means that if two lines intersect at (−6, 4), then (−6, 4) is the solution to the system of equations.
This means that if you substitute −6 for x and 4 for y in the equations, both equations will be true.
### Explanation:
To confirm that (−6, 4) satisfies (y = frac{1}{3}x + 6):
1. Substitute x = −6 into the equation:
[
y = frac{1}{3}(-6) + 6 = -2 + 6 = 4
]
2. Since substituting gives us y = 4, (−6, 4) indeed satisfies the equation.
This process shows that the point is where both lines meet in a system of equations.