Topic 4 Proctice What is the solution to the system of equations? \( y=\frac{1}{8} x-1 \) \( -5 x+4 y=-13 \)

To solve the system of equations, you can substitute the expression for \( y \) from the first equation into the second equation. Substituting gives you: \[ -5x + 4\left(\frac{1}{8}x - 1\right) = -13 \] Now solve for \( x \). Distributing \( 4 \) gives: \[ -5x + \frac{1}{2}x - 4 = -13 \] Combine like terms and solve for \( x \): \[ -\frac{9}{2}x = -9 \implies x = 2 \] Now plug \( x \) back into the first equation to find \( y \): \[ y = \frac{1}{8}(2) - 1 = \frac{1}{4} - 1 = -\frac{3}{4} \] So, the solution to the system of equations is \( (2, -\frac{3}{4}) \). Practicing these equations is like mental gymnastics! Just as athletes carefully refine their routines, math concepts become ingrained through repetition. Try varying the coefficients and constants to understand how changes affect solutions, all while keeping your problem-solving skills sharp! You can dive deeper into systems of equations with rich resources like Khan Academy or MIT’s OpenCourseWare. It's a treasure trove of practice problems and videos that walk you through everything, from the basics up to the more complex systems. Who knew learning could be this fun and engaging?