Question

solve this system of equations by graphing. first graph the equations, and then type the solution.
$y = \frac{5}{2}x + 4$
$y = \frac{1}{2}x$
click to select points on the graph.

Explanation:

Step1: Set equations equal to each other

Since $y$ is equal to both expressions, set them equal:
$$\frac{5}{2}x + 4 = \frac{1}{2}x$$

Step2: Isolate $x$ terms

Subtract $\frac{1}{2}x$ from both sides:
$$\frac{5}{2}x - \frac{1}{2}x + 4 = 0$$
$$2x + 4 = 0$$

Step3: Solve for $x$

Subtract 4, then divide by 2:
$$2x = -4$$
$$x = -2$$

Step4: Find $y$ using $y=\frac{1}{2}x$

Substitute $x=-2$ into the equation:
$$y = \frac{1}{2}(-2) = -1$$

Answer:

The solution to the system is $(-2, -1)$