Please solve these systems of equations.
4x+3y=45
2x+4y=38

x=33/5 and y=31/5

x=33/5 = 6.6

y=31/5 = 6.2

Step-by-step explanation:

4x+3y=45

2x+4y=38

​In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

4x+3y=45,2x+4y=38

To make 4x and 2x equal, multiply all terms on each side of the first equation by 2 and all terms on each side of the second by 4.

2×4x+2×3y=2×45,4×2x+4×4y=4×38

Simplify.

8x+6y=90,8x+16y=152

Subtract 8x+16y=152 from 8x+6y=90 by subtracting like terms on each side of the equal sign.

8x−8x+6y−16y=90−152

Add 8x to −8x. Terms 8x and −8x cancel out, leaving an equation with only one variable that can be solved.

6y−16y=90−152

Add 6y to −16y.

−10y=90−152

Add 90 to −152.

−10y=−62

Divide both sides by −10.

y=31/5

Substitute 31/5 for y in 2x+4y=38. Because the resulting equation contains only one variable, you can solve for x directly.

2x+4×(31/5)=38

Multiply 4 times 31/5.

2x+125/5=38

Subtract 124/5 from both sides of the equation.

2x=66/5

Divide both sides by 2.

x=33/5,y=31/5

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0