Jackson has 1 cup of butter. If he wants to use all the butter, how many batches of brownies can he make?
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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 =
x - 
Since both equations equal y, you can set them equal to each other and solve for x.
9x - 5 =<span>x - 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 = </span>
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(<span>) - y = 5 Multiply
</span>
- y = 5 Subtract <span> from both sides
</span>-y = <span>0.21276595744 (I had to convert it to a decimal) Divide both sides by -1
y = -</span><span>0.21276595744
So, the answer to the system is (</span>0.53191489361, -<span>0.21276595744)</span>
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 =
Since both equations equal y, you can set them equal to each other and solve for x.
9x - 5 =<span>
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 = </span>
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(<span>
</span>
</span>-y = <span>0.21276595744 (I had to convert it to a decimal) Divide both sides by -1
y = -</span><span>0.21276595744
So, the answer to the system is (</span>0.53191489361, -<span>0.21276595744)</span>