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 =
`(7)/(6)`x -
`(5)/(6)`

Since both equations equal y, you can set them equal to each other and solve for x.

9x - 5 =
`(7)/(6)`x -
`(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 =
`(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(
`(25)/(47)`) - y = 5 Multiply

`(225)/(47)` - y = 5 Subtract
`(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)