Answer:
The answers are:
[tex]x=2\\y=-1[/tex]
Step-by-step explanation:
In order to determine the solution for x and y, we have to solve both equations. We use the elimination method, where we eliminate the same variable in both equations.
In this method, we need to have the same coefficient in the eliminated variable, but different sign.
In this case, we choose to eliminate "x" variable. The minimum common multiple (mcm) between the coefficients of "x" is 6. So the first equation is multiplied by 3 and the second equation is multiplied by -2.
[tex]2x-5y=9\\3x+4y=2\\\\(3)*2x-(3)*5y=(3)*9\\(-2)*3x+(-2)*4y=(-2)*2\\\\6x-15y=27\\-6x-8y=-4\\\\-23y=23\\y=-\frac{23}{23} \\y=-1[/tex]
Then, we replace the value of "y" in any equation.
[tex]2x-5*(-1)=9\\2x+5=9\\2x=9-5\\2x=4\\x=\frac{4}{2}\\x=2[/tex]
Finally, the solution for both variables is:
[tex]x=2\\y=-1[/tex]
