Question

Solve the simultaneous equations:
5x+3y=12
2x+y=5

Answer 1

5x+3y=12
2x+y=5

Change the second equation to y=-2x+5. Now substitute this into the first equation:

5x+3(-2x+5)=12
5x-6x+15=12
-x+15=12
-x=-3
x=3

Now you can find y.
y=-2x+5
y=-2(3)+5
y=-1

Answer 2

I will use the substitution method, but you can also use elimination and matrix.

1. Solve for y in 2x+y=5
2x+y=5
y=5-2x

2. Substitute y=5-2x into 5x+3y=12
5x+3y=12
5x+3(5-2x)=12
5-x=12

3. Solve for x in 15-x=12
15-x=12
-x=12-15
-x=-3
x=3

4. Substitute x=3 into y=5-2x
y=5-2x
y=5-2*3
y=-1

5. Therefore,
x=3
y=-1

Have a nice day :D