Answer:
1.) x=1; y=1
2.) x=1; y=5
3.) No solution
Explanation:
1.) To start off with number one, we see that in both equations the x and y are positive, and the sums aren't equal to each other, this means we have to do something to make them equivalent. For example, we can multiply the top equation by 8 and the bottom equation by 7, so we get the equations 32x + 24y = 56 and the bottom equation to be 21x+35y=56. From here we can just make the equations equal each other to get 32x+ 24y = 21x +35y. From here we can just get a certain amount of x to equal certain amount of y by taking away the smaller amount of each and bringing it to the other side by subtracting. From that we get 11x = 11y. We can simplify this to be x=y. Now we can substitute either x or y in either equation to get 4x + 3(x) = 7. Then you solve algebraically and you get x=1. Now since we established that x was already equal to y, both x AND y are equal to 1.
2.) For this problem, we have an x that is negative in one equation and positive in the other. This means we can use the method of multiplying the bottom equation by 3 to get 3x +3y = 18. Now we are able to add both equations to each other crossing out the x's because they cancel out. From this we get 4y=20, Which means y=5. We can now plug this back into the equation to get x+(5) = 6. Which means y=5 and x=1.
3.) For this problem, we have both equations equal to y. However the x's are also equal to each other. Meaning if we were to solve them like in problem one, we would get the issue of cancelling the x's out and just getting 13/2=9/2 which is a problem because they do not equal each other. But, we can notice that both of the given systems are linear lines, meaning we could plot them off a graph. But to save time, we can notice that both equations have the exact same slope but different starting positions. Meaning that both lines would be parallel to each other. Since both lines are parallel to each other, There will never be an intersection, or answer between them. Making x and y null (no answer)