Answer:
The answers are x=4 and y=1
Step-by-step explanation:
I can only assume that the methods of solving a system of equations that you have learned are: elimination and substitution
Elimination works well when one of the variables have the same coefficient. As this system does not have that, this looks like a good situation to use substitution.
To solve a system of equation with substituiton, we first have to solve one of the equations for a variable. The next step is to substitute the value for the variable that we found into the other equation to find the numerical value of one variable. Then you can substutute this value into the solved equation for the other variable.
Let's get started by solving the second equation for y (It doesn't matter which one that you work with first)
[tex]3x-2y=10\\\\3x=2y+10\\\2y=3x-10\\\\y=\frac{3x-10}{2}[/tex]
Now, we can substitute in our value for y into the first equation
[tex]2x+5y=13\\\\2x+5(\frac{3x-10}{2})=13\\\\2x+\frac{15x}{2}-\frac{50}{2} =13\\\\2x+7.5x-25=13\\\\9.5x=38\\\\x= 4[/tex]
Now, we can substitute x=4 into our equation for y to find its value
[tex]y=\frac{3x-10}{2} \\\\y=\frac{3(4)-10}{2}\\\\y=\frac{12-10}{2} \\\\y=\frac{2}{2}\\\\y=1[/tex]
While we have our answer, I always like to substitute these value into one of the equations to make sure that it is a solution for the equation to check the answer is correct.
[tex]2x+5y=13\\\\2(4)+5(1)=13\\\\8+5=13\\\\13=13[/tex]
Since we got the same answer on both sides of the equals sign, we know that these values for x and y are solutions to this system of equations.
The answers are x=4 and y=1
