Solve the following system of equations.

1 answer:

4 0

There a number of methods in solving a system of equations. These methods are the substitution method, solving by graphing, gaussian elimination and by elimination method. For this case, we use the substitution method. To do this, we write one of the equation in a way where one variable is left on one side. We do as follows:

<span>−0.9x+0.5y=3.9
0.5y = 3.9 + 0.9x
y = 3.9/0.5 + 0.9x/0.5
y = 7.8 + 1.8x

Then, we subsitute this equation to variable y in the second equation.
</span>0.4x+1.5(7.8 + 1.8x)=−6.9

Then, we solve for x
0.4x+1.5(7.8 + 1.8x)=−6.9
0.4x+11.7 + 2.7x=−6.9
3.1x = -18.6
x = -6

We substitute this value of x, to the first equation to solve for y
y = 7.8 + 1.8x
y = 7.8 + 1.8(-6)
y = -3

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The hypotenuse of a right triangle measures 18 cm and one of its legs measures 12 cm. Find the measure of the other leg. If nece

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Answer:

16 cm

Step-by-step explanation:

A right triangle, with the hypotenuse = 18, one side = 7, and the other side = x.

Since this is a right triangle, use the pythagorean theorem to find the value for x.

let a = 7 for one side, and let c = 18 for the hypotenuse. And, let c = x for the other side.

The pythagorean theorem is: c^2 = a^2 + b^2.

18^2 = 7^2 + x^2324 = 49 +x^2

x^2 = 324 - 49 = 275So, x = sqrt(275) = 16.5 cm