b Solve the given system by setting the equations equal to each other.
A
a (4,5)
B
b Yes, see solution.
Practice makes perfect
a The point of intersection of a system is the x- and y-coordinates where the lines cross. We can determine this point from a graph by looking at the coordinates where the graphs intersect.
From the graph, we can see that the lines cross at the point (4,5).
b To verify or to find an exact solution, we can solve the system algebraically. It is possible to solve the given system algebraically by using the Substitution Method.
y=x+1 y=6- 14x
To solve the system we can substitute (x+1) for y in the second equation and solve for x. Once we know x, we can substitute that value into either equation to solve for y.
The x-coordinate of the solution to the system is 4. To determine the corresponding y-value, we can substitute x=4 into the first equation and solve for y.
