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<p>Graph of 2 lines, origin O. Horizontal axis, scale negative 25 to 25, by 5’s. Vertical axis, scale negative 20 to 20, by 5’s. A line is labeled y equals negative x plus 10. Another line is labeled y equals 2 x plus 4. The lines intersect at the point 2 comma 8.</p>
Estos son tres sistemas de ecuaciones. Encuentra la solución de cada sistema.
Empareja cada gráfica con un sistema de ecuaciones. Después usa las gráficas para comprobar que tus soluciones son razonables.
<p>A graph with two lines, in the x y plane, origin O. The graph has a scale of negative 25 to 25 on both the x and y axis. One line slants downward and right. It crosses the x axis at 10 and the y axis at 20. Another line slants upward and right. It crosses the y axis at 5. It crosses the x axis to the left of the origin. </p>
<p>A graph with two lines, in the x y plane, origin O. The graph has a scale of negative 25 to 25 on both the x and y axis. One line slants upward and right. It crosses the y axis between 25 and 30. It crosses the x axis between negative 10 and negative 15. Another line slants upward and right. It crosses the y axis between 10 and 15. It crosses the x axis between negative 20 and negative 25. </p>
<p>A graph with two lines, in the x y plane, origin O. The graph has a scale of negative 25 to 25 on both the x and y axis. One line slants upward and right. It crosses the x axis between 0 and 5. It crosses the y axis between 0 and negative 5. Another line slants upward and right. It crosses the x axis at 5 and the y axis at negative 10. </p>
estamos buscando un par de valores
Por ejemplo, considera el siguiente sistema de ecuaciones:
Como el valor de
Podemos resolver la ecuación para encontrar el valor de
Pero esto es solo la mitad de lo que estamos buscando: sabemos el valor de
Como ambas ecuaciones tienen el mismo valor de
En ambos casos encontramos que
<p>Graph of two lines line, origin O, with grid. Horizontal axis, x, scale negative 4 to 1, by 1s. Vertical axis, y, scale negative 1 to 4, by 1’s. The lines intersect at the point negative 2 comma 2. </p>
En general, un sistema de ecuaciones lineales puede tener: