Question

Examine the system of equations. Do you think the lines will intersect? Explain.

Answer 1

Considering the definition of a system of linear equations, the lines intersects at the point (0,-7).

System of linear equations

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are fulfilled. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

The unknowns established in a system represent the point where the lines intersect in a Cartesian plane (x,y).

This case

The system of equations to solve is:

$\left \{ {{y=2x-7} \atop {y=x-7}} \right.$

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, the "y" variable is already isolated in the first equation. Substituting in the second equation you get the expression:

2x -7= x-7

Solving:

2x -x= -7 + 7

x= 0

Substituting this value in the first equation you obtain the value of y:

y=2×0 -7

y= 0 -7

y= -7

So, the solution of the system of equations is (0,-7). That is, the lines intersects at the point (0,-7).

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