Which equation is formed from the two equations? 3x-7=11 and 4y+3=1
The Correct Answer and Explanation is:
Let’s start by analyzing the two given equations:
- 3x – 7 = 11
- 4y + 3 = 1
Step 1: Solve for x in the first equation.
The first equation is 3x – 7 = 11. To solve for x, follow these steps:
- Add 7 to both sides of the equation to isolate the term with x: 3x−7+7=11+7⇒3x=183x – 7 + 7 = 11 + 7 \quad \Rightarrow \quad 3x = 183x−7+7=11+7⇒3x=18
- Now, divide both sides of the equation by 3 to solve for x: 3×3=183⇒x=6\frac{3x}{3} = \frac{18}{3} \quad \Rightarrow \quad x = 633x=318⇒x=6
Step 2: Solve for y in the second equation.
The second equation is 4y + 3 = 1. To solve for y, follow these steps:
- Subtract 3 from both sides of the equation to isolate the term with y: 4y+3−3=1−3⇒4y=−24y + 3 – 3 = 1 – 3 \quad \Rightarrow \quad 4y = -24y+3−3=1−3⇒4y=−2
- Now, divide both sides by 4 to solve for y: 4y4=−24⇒y=−12\frac{4y}{4} = \frac{-2}{4} \quad \Rightarrow \quad y = -\frac{1}{2}44y=4−2⇒y=−21
Step 3: Combine the results.
From the first equation, we found that x = 6. From the second equation, we found that y = -1/2.
Thus, the values of x and y that satisfy both equations are x = 6 and y = -1/2. If we wanted to express these results as a combined equation, we can state:(x,y)=(6,−12)(x, y) = (6, -\frac{1}{2})(x,y)=(6,−21)
This pair represents the solution to the system of equations. In this case, there is no direct way to combine the two original equations into a single equation because they are not related in a way that would allow such simplification. The system represents two independent relationships that give the values of x and y when solved.
