Question

A system of linear equations in two variables is the collection of two linear equations in two variables considered simultaneously. B. A system of linear equations in two variables must have at least one solution. C. It is possible for a system of linear equations in two variables to have infinitely many solutions. D. The solution to a system of equations in two variables is the set of all ordered pairs for which both equations are true.

Answer 1

Complete Question:

Which of the following statements is not true?

Choose the incorrect statement below.

Answer:

B. A system of linear equations in two variables must have at least one solution.

Step-by-step explanation:

A linear function has a positive relationship and as such an increase in one variable (input variable) causes an increase in the other variable (output variable) i.e the variables are directly proportional. Thus, the graph of a linear function is a straight-line and its slope is always constant.

Similarly, a linear equation is an algebraic equation of the first order with two variables and each of its term having an exponent of one.

Generally, a system of linear equations in two variables must have at least two solution.

For example, y = 2x + 1 is a linear equation.

a. To find the value of y;

When x = 0

y = 2(0) + 1

y = 2 + 1

y = 3

b. To find the value of x;

When y = 0

0 = 2x + 1

2x = -1

x = -½