Answer:
x = 18/25, y = -198/25
Step-by-step explanation:
Given the system of equations:
2x – y = 13x
-3x + 2y= -18
You can combine these two equations effectively by multiplying the first equation by 2, and adding because -2y and 2y will cancel out when added. So you will be left with only x terms
( 2x - y = 13x ) × 2
+ -3x + 2y = -18
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2(2x) - 3x + 2(-y) + 2y = 2(13x) - 18
4x - 3x - 2y + 2y = 26x - 18
x + 0 = 26x - 18
x = 26x - 18
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[Then use the properties of equality to simplify the expressions in the equation to derive the value of x]
x - x = 26x - 18 - x (subtraction property of equality)
0 = 25x - 18
0 + 18 = 25x - 18 + 18 (addition property of equality)
18 = 25x
18 / 25 = 25x / 25 (division property of equality)
18 / 25 = x
x = 18 / 25 (symmetric property of equality)
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Now with the value of x, we can find the value of y by substituting the value of x into the variables of the top equation {2x – y = 13x} because this involves the simpliest steps.
Given x = 18 / 25.
2x – y = 13x → 2x – y + y = 13x + y → 2x = 13x + y → 2x – 13x = 13x + y – 13x → -11x = y → y = -11x.
Now that we know y = -11x, y = -11(18/25) which is - (11 × 18) / 25 = -198/25
