Manori’s bag has 10cent and 20cent coins. She has 202 coins with a total value of $31.90. How many 20cent coins does manori have?

a = 85 10cent coins

b = 117 20cent coins

a = 10c coins

b = 20c coins

$31.90 = c3190

a + b = 202 => a = 202 - b

10a + 20b = 3190

10(202 - b) + 20b = 3190

2020 - 10b + 20b = 3190

10b = 3190 - 2020

10b = 1170

b = 117 (20cent coins)

a = 202 - 117

= 85 (10cent coins)

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

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step-by-step explanation: