Solve the system of equations.

7x−3y=20
y=5x−4

PLEASE HELP!!! THANKS

ANSWER:

x = -1

y = -9

STEP ONE (FINDING X):

Well, we have one equation, 7x − 3y = 20, which has unknown y and x values, and another, y = 5x − 4, where it is given a value that y is equal to. plug that into the original equation and solve for x.

7x − 3y = 20 --> 7x − 3(5x − 4) = 20

To Solve:

7x − 3(5x - 4) = 20  - DISTRIBUTE 3 into 5x - 4

7x − 15x − 12 = 20 - COMBINE like terms

-8x - 12 = 20 - SUBTRACT 12 from both sides

-8x = 8 - DIVIDE both sides by -8

x = -1

STEP TWO (FINDING Y):

So, now we have our x value -- but we still need our Y value. To do this, let's plug our value for x (-1) into the equation y = 5x − 4 so we can find what our value of y is.

y = 5x − 4 --> y = 5(-1) − 4

To Solve:

y = 5(-1) − 4 - MULTIPLY 5 by -1

y = -5 - 4 - SUBTRACT 4 from -5

y = -9

So, we now know our y value is -9, the last step is to check work.

STEP THREE (FINDING Y):

To know if your found values are correct, plug them into 7x − 3y = 20. If the answer is, in fact, equal to 20 we know our answers are correct.

7x − 3y = 20 --> 7(-1) − 3(-9) = 20

To Solve:

7(-1) − 3(-9) = 20 - MULTIPLY 7 by -1 and 3 by -9

-7 - − -27 = 20 - SUBTRACT -7 by -27

20 = 20 (since the negatives cancel each other out)

FINAL NOTE: Since we have a true value of 20 = 20, We know the values we found are correct. The first time around I'd solved this, I found my values were wrong (I multiplied 4x4 instead of 3x4 in the first step of solving for x, making my answer 16. This messed up my answers, giving me -14 for y and -2 for x!) Which is why checking your work is always a good idea :-)

it increases the mean value of the prizes.

step-by-step explanation: