Respuesta :
we will use the delete method
fist, We need an equation to have the variable with the same number but with the opposite sign, for this we can multiply the entire equation by a constant
will use the first equation
[tex]-4x-3y=-26[/tex]we can multiply with -5/4 to turn the -4 into 5
[tex]\begin{gathered} -4x(\frac{-5}{4})-3y(\frac{-5}{4})=-26(\frac{-5}{4}) \\ \\ 5x+\frac{15}{4}y=\frac{65}{2} \end{gathered}[/tex]then, we will add the two equations
[tex]\begin{gathered} 5x+\frac{15}{4}y=\frac{65}{2}\text{ +} \\ \\ -5x+2y=-21 \\ ----------------- \\ (5-5)x(\frac{15}{4}+2)y=(\frac{65}{2}-21) \end{gathered}[/tex]we can simplify the equation
[tex]0x+\frac{23}{4}y=\frac{23}{2}[/tex]and solve Y
[tex]\begin{gathered} y=\frac{23\times4}{23\times2} \\ y=\frac{4}{2} \\ y=2 \end{gathered}[/tex]having Y we can replace in any initial equation and solve for X
I will use the second equation
[tex]\begin{gathered} -5x+2y=-21 \\ -5x+2(2)=-21 \\ -5x+4=-21 \\ -5x=-21-4 \\ -5x=-25 \\ x=\frac{-25}{-5} \\ x=5 \end{gathered}[/tex]and the solution is (5,2) or x=5 and y=2
