Linear Equations in Two Variables
Gujarat Board · Class 9 · Mathematics
Flashcards for Linear Equations in Two Variables — Gujarat Board Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
What is a linear equation in one variable? Give an example.
Answer
A linear equation in one variable is an equation with only one unknown variable and can be written in the form ax + b = 0, where a ≠ 0. Example: 2x + 5 = 0 or x + 1 = 0. Such equations have a unique s
Define a linear equation in two variables.
Answer
A linear equation in two variables is any equation that can be written in the form ax + by + c = 0, where a, b, and c are real numbers, and a and b are not both zero. Examples: 2x + 3y = 5, x - 4y + 7
Write the equation 2x + 3y = 4.37 in the standard form ax + by + c = 0 and identify a, b, and c.
Answer
2x + 3y = 4.37 can be written as 2x + 3y - 4.37 = 0. Here, a = 2, b = 3, and c = -4.37.
Convert the equation x - 4 = 3y to standard form and identify the coefficients.
Answer
x - 4 = 3y can be written as x - 3y - 4 = 0. Here, a = 1, b = -3, and c = -4.
How can you write x = -5 as a linear equation in two variables?
Answer
x = -5 can be written as 1·x + 0·y + 5 = 0 or simply x + 0y + 5 = 0. Here, a = 1, b = 0, and c = 5.
Express y = 2 as a linear equation in two variables in standard form.
Answer
y = 2 can be written as 0·x + 1·y - 2 = 0 or simply 0x + y - 2 = 0. Here, a = 0, b = 1, and c = -2.
What is a solution of a linear equation in two variables?
Answer
A solution of a linear equation in two variables is an ordered pair (x, y) of values that satisfies the equation when substituted. For example, (3, 2) is a solution of 2x + 3y = 12 because 2(3) + 3(2)
Check if (1, 4) is a solution of the equation 2x + 3y = 12.
Answer
Substituting x = 1 and y = 4: 2(1) + 3(4) = 2 + 12 = 14. Since 14 ≠ 12, (1, 4) is NOT a solution of 2x + 3y = 12.
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