PLS HELP algebra 2, linear equations

Question

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Solve the system using elimination.

2x-3y=-1

3x+4y=7

Answer 1

Solve the system using elimination.

2x – 3y = –1

3x + 4y = 7

If required to use elimination then you need the same coefficient (or its negative) for either x or y so that you can

1. add or subtract the equations in order to
2. eliminate one variable and solve for the other

One way to accomplish this for the system given is to

1. multiply the top equation by 4, then
2. multiply the bottom equation by 3, then
3. add the two equations together to eliminate y and solve for x.

4(2x – 3y = –1) gives 8x – 12y = –4

3(3x + 4y = 7) gives 9x + 12y = 21

Adding the resulting equations together gives

8x + 9x = –4 + 21

Now solve for x.

Then plug this value of x into either 2x – 3y = –1 or 3x + 4y = 7 and solve for y.

Hope this helps. Add a comment if you have any questions.

Answer 2

The idea behind elimination is that you add the 2 equations together so that one goes to zero. This means that one variable has to have the same coefficient and opposite signs.

Since y has opposite signs, I will focus on that one. To get the same coefficient, you have to pick terms to multiply by. The lowest coefficient I can get with a 4 and 3 is 12. So multiply accordingly.

4(2x-3y=-1)

3(3x+4y=7)

8x-12y=-4

9x+12y=21 Add these together

17x=17 Divide

x=1

Now plug this in to either equation to solve for y

3(1)+4y=7 Subtract 3

4y=4 Divide

y=1

Bring x and y together (1,1) is the solution