Example Question - inconsistent equations
Here are examples of questions we've helped users solve.
Solving an Equation with No Solution
Para resolver la ecuación que se muestra en la imagen, seguiré los pasos uno a uno en español. La ecuación es: 5 - 2(1 - x) = 2x - 3 Primer paso, distribuir el -2 en la expresión entre paréntesis: 5 - 2*1 + 2x = 2x - 3 Se simplifica multiplicando: 5 - 2 + 2x = 2x - 3 Ahora, combinamos términos semejantes: 3 + 2x = 2x - 3 Luego, restamos 2x de ambos lados para obtener los términos "x" en el mismo lado: 3 = -3 Como acabamos de obtener una declaración falsa (3 no es igual a -3), esto indica que la ecuación no tiene solución. El resultado es que la ecuación es inconsistente y no existen valores de x para los cuales la ecuación original sea verdadera.
Parallel Lines and Inconsistent Equations
The equations provided are: 1) \( y = -\frac{5}{4}x + 8 \) 2) \( y = -\frac{5}{4}x - 9 \) To solve these equations, we need to find the values of \(x\) and \(y\) where both equations are satisfied, meaning where the lines intersect if these were graphed. However, when we observe the equations, we notice that the coefficients of \(x\) in both equations are identical, and the constants are different. This means that the lines are parallel and never intersect. These equations represent parallel lines because they have the same slope, which is \(-\frac{5}{4}\), but different y-intercepts. The y-intercept of the first equation is 8, and the y-intercept of the second equation is -9. Since the lines never meet, there is no solution to this system of equations—they are inconsistent. Therefore, there are no specific values of \(x\) and \(y\) that would solve both equations simultaneously.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com