Solving two equations in two variables, one of them is of the first degree and the other is of the second degree — الرياضيات الصف الثالث الإعدادي لغات

الدرس ده من وحدة «Equations» فى مادة الرياضيات لـالصف الثالث الإعدادي لغات على منصة دروسات.

الدرس متاح بالاشتراك: ترم كامل أو المادة لوحدها.

ملخص الدرس

This lesson focuses on solving systems where one equation is linear (first degree) and the other is quadratic (second degree). The method introduced is substitution: solve the linear equation for one variable, then substitute into the quadratic equation to obtain a single equation in one variable. The lesson demonstrates the method through two worked examples: a system with y + 2x + 1 = 0 and 4x² + y² - 3x = 1, which yields two solutions, and a geometry problem where a rectangle with perimeter 14 cm and area 12 cm² is solved, yielding dimensions 3 cm × 4 cm. The substitution method reduces the system to a quadratic equation that can be solved by factoring or the quadratic formula.

هتتعلم إيه فى الدرس ده

• Identifying first-degree vs. second-degree equations in two variables
• The substitution method for solving mixed systems
• Substituting a linear expression into a quadratic equation
• Solving the resulting quadratic equation by factoring
• Finding ordered pair solutions by back-substitution
• Real-world application: rectangle dimensions from perimeter and area
• Understanding that mixed systems can yield multiple solutions