1. solve the system using elimination -4x + 4y = -8 x = 4y = -7 2. what is the solution of the system? write answer in (x, y) form. -8x + 2y = -26 -5x - 5y = -10 3. solve the system using an equivalent system. 3x - 5y = 9 3x - y = -3 4. what are the solutions of the following systems? -x + y = -2 4x - 4y = 8

1. (7.4,3.6)

2. (3,-1)

3. (-2,-3)

4. Infinite number of solutions.

Step-by-step explanation:

We can solve systems of equations 3 ways: graphing, substitution, and elimination. We will solve 1-2, 4 using substitution and 3 with elimination.

1. Since x=4y-7, we substitute it in for x . It's better than elimination because of how it is set-up unless there is a typo.

So -4x+4y=-8 becomes -4(4y-7)+4y=-8. We simplify to -14y+28+4y=-8. We add like terms to get -10y+28=-8. We now solve for y by subtracting 28 and dividing by -10.-10y+28-28=-8-28-10y=-36y=3.6We substitute y=3.6 into x=4y-7. x=4(3.6)-7=14.4-7=7.4

2.  Since none of the coefficients of x & y are the same, we will rearrange and substitute.

-8x+2y=-26 becomes 2y=8x-26 by adding 8x to both side.We divide by 2. y=4x-13.We substitute into -5x-5y=-10. -5x-5(4x-13)=-10We simplify to -5x-20x+65=-10We add like terms. -25x+65=-10We now solve for x by subtracting 65 and dividing by -25.-25x+65-65=-10-65-25x=-75x=3We substitute x=3 into -8(3)+2y=-26-24+2y=-262y=-2y=-1

3. We can solve this system through elimination. We subtract or add the equations when the coefficients are the same to eliminate one variable.

We susbstitute y=-3 into one of the equations 3x-(-3)=-3.3x=-6x=-2

4. Since none of the coefficients of x & y are the same, we will rearrange and substitute.

-x+y=-2 becomes y=x-2We substitute into 4x-4(x-2)=8.Simplify 4x-4x+8=8.Add like terms 0x+8=88=8This is a true statement and a special solution. It means infinite number of solutions.