Type the correct answer in each box. If necessary, use / for the fraction bar(s). Find the solution for this system of equations.

12x + 15y = 34
-6x + 5y = 3

x=5/6 and y=8/5

(5/6 , 8/5)

Step-by-step explanation:

You can use the elimination method! The point of this method is to add or subtract one equation from the other, multiplying them by constants if necessary, to cancel out one variable so you can solve for the other. Then, you can plug the value you got for your solution into either equation to solve for the other. I'll demonstrate.

Look at the two equations and the coefficients of both variables. You have 12x and -6x -- 6*2=12, so this is perfect. (You could also eliminate the y because 5*3=15, but I'll show you by eliminating the x instead.)

Here's what that looks like:

(-6x+1y=3)2

-12x+10y=6

So we just multiplied the second equation by 2 on both sides. Let's see how that helps us.

12x+15y=34

-12x+10y=6

If we add the two equations now, x will be canceled out and we can solve for y.

   12x+15y=34

+(-12x+10y=6)

     0x+25y=40

           25y=40

0x=0, so we can get rid of the x. Now, we need to solve for y.

25y=40

y=40/25

You probably know how to simplify fractions, so divide both the numerator and the denominator by 5 to get y=8/5.

Now you can use this value in either equation and solve for x. I'll use the first. (This is called substitution.)

12x+15(8/5)=34

12x+3(8)=34 <-- What I did here is cancel out the 5 in the denominator with 15 to leave 3, because 5*3=15.

12x+24=34

12x=10

x=10/12

x=5/6 (Divide the numerator and denominator by 2.)

You can write your answer as a point, too. (5/6 , 8/5)

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions