2x+y=3, 5x-2y=12 how to solve this

Start by getting one of the equations in terms of one variable, in this case lets put the first equation in terms of y

2x+y=3 ---> y=3-2x

now we plug that into the second equation

5x-2y=12 ---> 5x-2(3-2x)=12

we can then multiply and simplify

5x-2(3-2x)=12 ---> 5x-6+4x=12 ---> 9x-6=12 ---> 9x=18 ---> x=2

we can now plug x=2 into an equation to solve for y

2(2)+y=3 ---> 4+y=3 ---> y=-1

2x+y=3 =4x+2y=6
5x-2y=12. =5x-2y=12

9x=18: x=2
4+y=3:y=-1

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