Question 50291
10x+2y=7
y=-5x+3 
We can solve this system of equations using the elimination method.
But first we need to put each equation in standard form so that they look the same. You have...
10x + 2y = 7
y = -5x + 3
The top equation is already in standard form so we just need to get the -5x in the bottom equation on the left side by adding it from both sides.
10x + 2y = 7
5x + y = 3
Now we are ready to begin eliminating variables. 
First we need to decide which coefficiant to work with in order to cancel out or "eliminate" the other.
For instance, we have 10x and 5x.
What do we need to do to the 5x in order to cancel out the 10x?
What if we multiply the second (bottom) equation by -2? 
10x + 2y = 7
-2(5x + y = 3)
When we distribute, we get...
10x + 2y = 7
-10x - 2y = -6
Now we can add our system to solve the equation. Like so...
10x + 2y = 7
-10x - 2y = -6

We can write the answer as...
zero, 0 or empty set, { }. 
I hope this helps.