Question

Use substitution. 2x + 3y = 5 4x - y = 17 Use linear combinations: 2x + 3y = 5 4x - y = 17

Answer 1

I'll help you get started. To use substitution on the first pair of equations, we want to solve for one of the variables in one of the two equations. It looks like it would be easiest to solve for y in the second equation:
$4x-y=17$
$4x=17+y$
$4x-17=y$

Now we want to substitute this alternate version of y into the first equation:
$2x+3(4x-17)=5$.

I'll let you finish off that first one. The second problem asks to solve the two equations using linear combination. This means we want to add the two equations together and cancel out one of the variables. Again, it's easiest to cancel out the y since one is negative. First we want to take the second equation and multiply by 3 on both sides:
$3(4x-y)=3(17)$
$12x-3y=51$

Now we want to add both equations together. Add the left sides and the right sides on their respective sides of the equals sign:
$(2x+3y)+(12x-3y)=5+51$

You can finish that one as well. Your answers for both methods will be the same if you do everything right! Let me know if you have more questions