Solve the system of equations by eliminating the x variable

Solve the system of equations by eliminating the x variable: {2x 1+ 2y = -12 x + 3y = -10 (x, y) = Ron has 11 coins with a total value of $1.55. The coins are nickels and quarters. How many of each coin does he have? Ron has nickels and quarters.

Solution

17) Given two equations are 2x+2y=-12

x+3y=-10

Need to find the solution by eliminating x variable.

Multiply the second equation by 2

2(x+3y)=2(-10)

2x+6y=-20

Subtract first equation from the above equation.

2x+6y-2x-2y=-20+12

4y=-8 (i.e., x is eliminated)

y=-2

Substitute y=-2 in 2x+2y=-12

2x+2(-2) = -12

2x=-12+4=-8

x=-4

Therefore, x=-4 and y=-2

(x,y)=(-4,-2)

18) Given that 11 coins of nickles and quarters makes a total value of $1.55

20nickels =1doller.

1nickel = 1/20 dollers

1nickel = 0.05 doller

4quarters = 1doller

1quarter = 1/4 doller

1quarter = 0.25doller

Let there are x nickels then (11-x)quarters

x(0.05)+(11-x)(0.25) = 1.55

0.05x+11*0.25-0.25x = 1.55

0.05x-0.25x+11*0.25 = 1.55

-0.2x+2.75 = 1.55

2.75-1.55 = 0.2x

1.2 = 0.2x

12 = 2x

x=12/2

x=6

11-x=11-6=5

Therefore, Ron has 6 nickels and 5 quarters