Answer
One solution: (4,1) (x = 4, y = 1)
Work Step by Step
Equation 1: 3x - 5y = 7
Equation 2: 2x + y = 9
Solving this by elimination is the easiest route. It is simplest to multiply equation 2 by 5; this way, we will have a -5y and +5y to cancel out in both equations. Our new equation 2 is:
5(2x + y) = 5(9)
10x + 5y = 45 (distributive property, multiplication)
If we add equation 1 and our new equation 2, we get...
Equation 1: 3x - 5y = 7
Equation 2: + 10x + 5y = 45
13x + 0y = 52
The 0y can be eliminated, so we are left with 13x = 52. Dividing both sides by 13 gets x by itself, which equals 4 (52 divided by 13). To solve for the y-coordinate, plug x into either original equation and solve.
2(4) + y = 9 (plug x-value into original equation)
8 + y = 9 (multiply)
y = 1 (solve for y by isolating and subtracting 8 from each side)
There is 1 solution for the equations: (4,1), or x = 4, y = 1.
