ANSWER:
<em>x</em> = -1
<em>y = </em>-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 - <em>DISTRIBUTE 3 into 5x - 4</em>
7x − 15x − 12 = 20 - <em>COMBINE like terms </em>
-8x - 12 = 20<em> - SUBTRACT 12 from both sides </em>
-8x = 8 - <em>DIVIDE both sides by -8</em>
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 <em>- MULTIPLY 5 by -1</em>
y = -5 - 4<em> - SUBTRACT 4 from -5</em>
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 <em>- MULTIPLY 7 by -1 and 3 by -9</em>
-7 - − -27 = 20 <em>- SUBTRACT -7 by -27 </em>
20 = 20 <em>(since the negatives cancel each other out)</em>
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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 :-)
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