Systems of linear equations Questionbank

If you use substitution to solve the system below, which equation represents the correct first step after substituting the expression for $x$ into the second equation?

A nutritionist mixes Brand A juice (10% sugar) and Brand B juice (25% sugar) to create 5 litres of a mixture containing 16% sugar. If $x$ is the volume of Brand A and $y$ is the volume of Brand B, find the value of $y$.

A rectangular garden has a perimeter of 50 metres. The length $L$ is 5 metres less than three times the width $W$. Which system of equations correctly models this situation?

Consider the following system of linear equations:

Which of the following best describes the solution to this system?

A small business has fixed costs of $200 per day and a variable cost of $5 per item produced. They sell each item for $10. If $x$ is the number of items and $y$ is the total cost or revenue, which system of equations models the break-even point?

If a system of two linear equations in the form $y = mx + b$ has different gradients ($m_1 \ne m_2$), the system is classified as having:

To solve $3x + y = 10$ and $x - 2y = 1$ by substitution, one could isolate $y$ in the first equation to get $y = 10 - 3x$. Substituting this into the second equation results in which simplified one-variable equation?

Consider the following system of linear equations:

$\begin{cases} y = x + 1 \\ y = 4 - 2x \end{cases}$

Which of the following statements is correct regarding the ordered pair $(1, 2)$?

In the modelling of a system where $x$ and $y$ represent the number of hours worked at two different jobs, the inequality $x + y \le 40$ typically represents a ____.

For the linear inequality $3x + 4y < 12$, which statement correctly describes the boundary line and its inclusion in the solution set?