Question

Use the drop-down menus to complete the statements below to answer this question: Can you determine whether a system of linear equations has a solution just by looking at the graph of the equations?


Six parts xD

Answer 1

• The coordinates of a point satisfies the equation of a line if the point lies on the line
• If a single point satisfies the equations of two lines, the point is on both lines, so the lines will intersect at that point.
• This means that each point where the two lines touch is a solution to the system of equations
• This means that if you substitute the x and y values of the point for x and y in the equations, both equations will be true

Explanation:

You haven't given any option. However, I have tried to complete this question according to what we know about system of linear equations. Suppose you have the following system of two linear equations in two variables:

$(1) \ y=3+2x \\ \\ (2) \ y=x$

The fist equation is the blue one and the second equation is the red one. Both have been plotted in the first figure below. As you can see, (-3, -3) is the point of intersection and lies on both lines. So this point is a solution of the system of equation and we can also say that it touches both lines. On the other hand, if you substitute the x and y values of the point for x and y in the equations, both equations will be true, that is:

$-3=3+2(-2) \therefore -3=-3 \ True! \\ \\ (2) \ -3=-3 \ True!$

Also, you can have a system with infinitely many solutions as the following:

$(1) \ y+2x=4\\ \\ (2) \ 2y+4x=8$

Here, every point that is solution of the first equation is solution of the second one. That is because both equations are basically the same. If we divide eq (2) by 2, then we get eq (1).

Learn more:

System of linear equations in real life problems: https://brainly.com/question/10412788

#LearnWithBrainly

Answer 2

Box one: on the line

Box two: on both lines; intersect

Box three: intersect; solution

Box four: true

I did it on I.M.