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.
Graph both equations on the same graph. Where they intersect is the solution to the system of equations
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.