\( 3 x-20 x-35=-26.5 \) 4. Kiran and Noah are trying to solve this system by substitution: \( \left\{\begin{array}{l}2 x+y=1 \\ 2 x+7 y=19\end{array}\right. \) Kiran's first step is to isolate \( y \) in the first equation to get \( y=1-2 x \). Noah's first step is to isolate \( 2 x \) inthe first equation tege \( 3 x=1-y \). Show thaitoth first steps can be used to solve the system and will yield the same solution.
Solución de tutoría real
Responder
Solución
¡Inicia sesión para desbloquear respuestas gratis!
Una plataforma de aprendizaje en la que confían millones de estudiantes y profesores reales.
Revisado y aprobado por el equipo de tutoría de UpStudy
Bonus Knowledge
To solve the first equation \( 2x + y = 1 \), Kiran correctly isolates \( y \) as \( y = 1 - 2x \). Substituting this into the second equation \( 2x + 7y = 19 \) gives us \( 2x + 7(1 - 2x) = 19 \). This leads to \( 2x + 7 - 14x = 19 \), simplifying to \( -12x = 12 \), resulting in \( x = -1 \) and subsequently \( y = 3 \) for a solution of \( (-1, 3) \). Noah's approach, isolating \( 2x \) from \( 2x + y = 1 \) to get \( 2x = 1 - y \), allows him to substitute into the second equation as well. Plugging \( 1 - y \) into \( 2x + 7y = 19 \) results in \( (1 - y) + 7y = 19 \). This simplifies to \( 1 + 6y = 19 \), yielding the same \( y \) value of \( 3 \) and confirming that both paths lead to the same solution \( (-1, 3) \).