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Can you determine whether a system of linear equations has a solution just by looking at the graph of the equations?

Updated April 20, 2025

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?

The coordinates of (−6, 4) satisfy the equation y = 1/3 x + 6 because (−6, 4) is on the graph of y = 1/3x + 6.

If (−6, 4) satisfies the equations of two lines, (−6, 4) is, so the lines will intersect at (−6, 4).

This means that if two lines intersect at (−6, 4), they are the solution to the system of equations.

This means that if you substitute −6 for x and 4 for y, the equations will be true.

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Quizzma TeamApril 20, 2025

Sure!

The completed statements would be:

The coordinates of (−6, 4) satisfy the equation y = 1/3 x + 6 because (−6, 4) is on the graph of y = 1/3x + 6.

If (−6, 4) satisfies the equations of two lines, (−6, 4) is a solution, so the lines will intersect at (−6, 4).

This means that if two lines intersect at (−6, 4), they are consistent and the solution to the system of equations.

This means that if you substitute −6 for x and 4 for y, the equations will be true.

Explanation: You can determine if a system of linear equations has a solution by looking at the graph. If the lines intersect at a point, that point is a solution to the equations. If the lines are parallel and do not intersect, the system has no solution. If they are the same line, there are infinitely many solutions.