Solve the following system of equations for x and y by cross multiplication: 11x + 5y – 7 = 0 and 6x – 3y – 21 = 0.
The Correct Answer and Explanation is:
To solve the system of equations by cross-multiplication, we start with the following system:
- 11x+5y−7=011x + 5y – 7 = 011x+5y−7=0
- 6x−3y−21=06x – 3y – 21 = 06x−3y−21=0
Step 1: Rearranging the equations
First, we rewrite both equations in a form that is suitable for cross-multiplication. This means isolating the constants on one side.
For the first equation: 11x+5y−7=0 ⟹ 11x+5y=7(Equation 1)11x + 5y – 7 = 0 \implies 11x + 5y = 7 \quad \text{(Equation 1)}11x+5y−7=0⟹11x+5y=7(Equation 1)
For the second equation: 6x−3y−21=0 ⟹ 6x−3y=21(Equation 2)6x – 3y – 21 = 0 \implies 6x – 3y = 21 \quad \text{(Equation 2)}6x−3y−21=0⟹6x−3y=21(Equation 2)
Now, we have the system: 11x+5y=711x + 5y = 711x+5y=7 6x−3y=216x – 3y = 216x−3y=21
Step 2: Cross-multiplication method
The method of cross-multiplication can be applied by treating this system as if it were two fractions. We first write both equations in the form of fractions: x7=y−3=z21\frac{x}{7} = \frac{y}{-3} = \frac{z}{21}7x=−3y=21z
