what does 3x-y=13 and 5x+3y=2 in linear system algebralically
please help me!
We need to determine the x and y values at the point
where these two lines intersect.
1) 3x - y = 13
2) 5x + 3y = 2
Using equation 1, solve for y in terms of x.
3x - y = 13
-y = -3x + 13
y = 3x - 13
Substitute that value of y into equation 2.
5x + 3y = 2
5x + 3(3x - 13) = 2
5x + 9x - 39 = 2
14x = 2 + 39
14x = 41
x = 41/14 <<<<<<<<<<<<<<<<<<
Plug that into equation 1 to solve for y.
3x - y = 13
3(41/14) - y = 13
123/14 - y = 13
-y = 13 - 123/14
y = -13 + 123/14
y = -182/14 + 123/14
y = -59/14 <<<<<<<<<<<<<<<<<<
Now, plug both values into equation 2 to check the answer.
5x + 3y = 2
5(41/14) + 3(-59/14) = 2
205/14 - 177/14 = 2
28/14 = 2
2 = 2