Question

9x-y=5 7x-6y=5 Solve the system by the substitution method

Answer 1

  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)