It is required to check if the point (5,-2) is a solution to the system of equations:
[tex]\begin{cases}5x-y={27} \\ -3x+4y={-23}\end{cases}[/tex]
To do this, substitute the point into the equations and check if it satisfies both equations.
Substitute (x,y)=(5,-2) into the first equation:
[tex]\begin{gathered} 5(5)-(-2)=27 \\ \Rightarrow25+2=27 \\ \Rightarrow27=27 \end{gathered}[/tex]
Notice that the point satisfies the first equation.
Check for the second equation by substituting (x,y)=(5,-2) into the equation:
[tex]\begin{gathered} -3(5)+4(-2)=-23 \\ \Rightarrow-15-8=-23 \\ \Rightarrow-23=-23 \end{gathered}[/tex]
Notice that the point also satisfies the second equation.
It follows that the point (5,-2) is a solution to this system.
The answer is 'true'.
