Substitution method: from first equation y = 5x - 8. In the second equation this gives
25x - 5(5x - 8) = 32 ie 25x - 25x + 40 = 32 ie 40 = 32 which is not possible, so the
system has no solution.
Multiplication method: first equation times 5 gives 25x - 5y = 40, but second equation gives 32 as the value of the identical expression. No solution.
x=3
x = y = 3
The solution of a system of linear equations is a pair of values that make both of the equations true.
A system of equations will have no solutions if the line they represent are parallel. Remember that the solution of a system of equations is physically represented by the intersection point of the two lines. If the lines don't intersect (parallel) then there can be no solution.
A system of linear equations can only have: no solution, one solution, or infinitely many solutions.
No solution
-1
7
x=3
x = y = 3
The pair of equations have one ordered pair that is a solution to both equations. If graphed the two lines will cross once.
x = 1 and y = 2
That system of equations has no solution. When the two equations are graphed, they turn out to be the same straight line, so there's no such thing as a single point where the two lines intersect. There are an infinite number of points that satisfy both equations.
there is no linear equations that has no solution every problem has a solution
Check your text book for how to solve it.
{-1,-2}
A system of equations with exactly one solution intersects at a singular point, and none of the equations in the system (if lines) are parallel.