
- Solve 2m + n = 2 and 3m - 2n = 3 using substitution.

We can use the substitution method to solve linear equations of this form. Let's solve for m & n.

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

Choose one of the equations and solve it for m by isolating m on the left-hand side of the equal sign.

Subtract n from both sides of the equation.

Divide both sides by 2.

Multiply 1/2 times -n+2.

Substitute
for m in the other equation, 3m-2n=3.

Multiply 3 times
.

Add
to -2n.

Subtract 3 from both sides of the equation.

Divide both sides of the equation by
, which is the same as multiplying both sides by the reciprocal of the fraction.

Substitute 0 for n in
. Because the resulting equation contains only one variable, you can solve for m directly.

The system is now solved.

Answer:
Step-by-step explanation:
For each game played the chance of winning is 0.05 and losing is 0.95.
If the student wins, they get $5 -$1 = $4, but they lose $1.
<u>Expected value is:</u>
It means you will make $0.75 per average game.
Answer:
x = 67.50 ft
Step-by-step explanation:
Consider, ΔMAB and ΔMNP,
∠M = ∠M (Common)
Given AB║NP and let MN as transversal,
∠MAB = ∠MNP (alternate angle)
Also, Given AB║NP and let MP as transversal,
∠MBA = ∠MPN (alternate angle)
Therefore, ΔMAB ≅ ΔMNP (By AAA similarity )
Thus, by CPCT,

consider first two ratios,

Substitute the values, MA = MN - AN = 49.5 ft

On solving for x , we get, x = 67.50 ft
Thus, value of x is 67.50 ft
Each ticket is $34 each
32+12+2x=112
44+2x=112
-44 -44
———————-
2x=68
— —
2 2
x=$34