Number and nature of solutions to linear systems

Interactive practice questions

The graphical solution of a system of two linear equations can be described as:

The point of intersection of two lines.

A

Any point that is at an equal distance from two lines.

B

The angle between two lines at their point of intersection.

C

The distance between the $y$y-intercepts of two lines.

D

The point of intersection of two lines.

A

Any point that is at an equal distance from two lines.

B

The angle between two lines at their point of intersection.

C

The distance between the $y$y-intercepts of two lines.

D
Easy
Less than a minute

How can we know whether a given ordered pair is a solution of a system of equations? Select all that apply.

We are going to determine whether the point $\left(5,2\right)$(5,2) is a solution of the system of equations:

$x+y=7$x+y=7

$x-y=3$xy=3

We are going to determine whether the point $\left(4,17\right)$(4,17) is a solution of the system of equations:

$y=6x-7$y=6x7

$4x+3y=67$4x+3y=67

Outcomes

10P.LR3.02

Solve systems of two linear equations involving two variables with integer coefficients, using the algebraic method of substitution or elimination