9x - y = 5
7x - 6y = 5
Solve both equations for one variable. I'll solve for y.
9x - y = 5 Subtract 9x from both sides
-y = -9x + 5 Divide both sides by -1
y = 9x - 5
7x - 6y = 5 Subtract 7x from both sides
-6y = -7x + 5 Divide both sides by -6
y = \(\frac{7}{6}\)x - \(\frac{5}{6}\)
Since both equations equal y, you can set them equal to each other and solve for x.
9x - 5 = \(\frac{7}{6}\)x - \(\frac{5}{6}\) Multiply both sides by 6 to eliminate the fractions
54x - 30 = 7x - 5 Subtract 7x from both sides
47x - 30 = -5 Add 30 to both sides
47x = 25 Divide both sides by 47
x = \(\frac{25}{47}\)
Now, plug that x-value into the x of either equation. I'll plug it into 9x - y = 5.
9x - y = 5 Plug in the x-value
9(\(\frac{25}{47}\)) - y = 5 Multiply
\(\frac{225}{47}\) - y = 5 Subtract \(\frac{225}{47}\) from both sides
-y = 0.21276595744 (I had to convert it to a decimal) Divide both sides by -1
y = -0.21276595744
So, the answer to the system is (0.53191489361, -0.21276595744)
