Solve:
2x+3y=102x+3y=10
5x+2y=19.55x+2y=19.5
We can solve this system of equations by elimination.
First, we need to multiply the first equation by 55 and the second equation by 22 to make the xx coefficient same for both equations:
5(2x+3y=10)5(2x+3y=10)
10x+15y=5010x+15y=50
2(5x+2y=19.5)2(5x+2y=19.5)
10x+4y=3910x+4y=39
Since the xx coefficient for both equations is now 1010, we can subtract the second equation from the first equation and simplify:
10x+15y-(10x+4y)=50-3910x+15y−(10x+4y)=50−39
10x+15y-10x-4y=1110x+15y−10x−4y=11
11y=1111y=11
y=1y=1
Now, we can substitute this yy value into one of the original equations and solve for xx, we'll use the first one:
2x+3(1)=102x+3(1)=10
2x+3=102x+3=10
2x=72x=7
x=7/2x=72
Therefore, our answer as a coordinate is (7/2,1)(72,1)
