Question

Linear equations in Two Variables

1. (-1, 4); x + y = 3
2. (0, 2); 2x - y = 2
3. (20, 30); 1/10 x + 1/5 y - 8
4. (0.3, -0.1); 200x - 100y = 10
5. (2/5, 1/4); 10x - 20y = -1

Answer 1

The linear equations from the given options are: Equation 2: 2x - y = 2, Equation 4: 200x - 100y = 1, and Equation 5: 10x - 20y = -1.

Step-by-step explanation:

Linear equations can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept. In order to determine if a given equation is linear, we need to check if it can be written in the form y = mx + b.

Let's check each equation from the options:

1. (-1, 4); x + y = 3
   Not linear because it cannot be written in the form y = mx + b.
2. (0, 2); 2x - y = 2
   Linear because it can be rearranged to the form y = mx + b, where m = 2 and b = -2.
3. (20, 30); 1/10 x + 1/5 y = 84
   Not linear because it cannot be written in the form y = mx + b.
4. (0.3, -0.1); 200x - 100y = 1
   Linear because it can be rearranged to the form y = mx + b, where m = -2 and b = -105.
5. (2/5, 1/4); 10x - 20y = -1
   Linear because it can be rearranged to the form y = mx + b, where m = 1/2 and b = 5/4.

So, the linear equations are:

• Equation 2: 2x - y = 2
• Equation 4: 200x - 100y = 1
• Equation 5: 10x - 20y = -1