Question

Determine the solution to the system of equations graphed below and explain your reasoning in complete sentences. Graph showing f of x equals absolute value of x minus 4, plus 2 and g of x equals 3x plus 2. The graphs intersect at the point 1 comma 5.

Answer 1

The system of equations consists of two equations: f(x) = |x - 4| + 2 and g(x) = 3x + 2. We need to find the value of x that satisfies both equations.

From the graph, we can see that the two graphs intersect at the point (1, 5). This means that f(1) = g(1) = 5.

Substituting x = 1 into the equation for g(x), we get:

g(1) = 3(1) + 2 = 5

Therefore, we have found one solution to the system of equations: x = 1.

Now we need to check whether this value of x also satisfies the equation for f(x):

f(1) = |1 - 4| + 2 = 3 + 2 = 5

Since f(1) = g(1) = 5, we have found the solution to the system of equations.

Therefore, the solution to the system of equations is x = 1, and the point of intersection is (1, 5).