Find the solution of the system of equations.6, x, plus, y, equals, 306x+y=30minus, 2, x, minus, 5, y, equals, 18−2x−5y=18
Question
Find the solution of the system of equations.6, x, plus, y, equals, 306x+y=30minus, 2, x, minus, 5, y, equals, 18−2x−5y=18
Solution
The system of equations is:
- 6x + y = 30
- -2x - 5y = 18
Let's solve it step by step:
Step 1: Multiply the first equation by 5 and the second equation by 1 to make the coefficients of y the same in both equations. This gives us:
30x + 5y = 150 -2x - 5y = 18
Step 2: Add the two equations together:
(30x - 2x) + (5y - 5y) = 150 + 18 28x = 168
Step 3: Divide both sides of the equation by 28 to solve for x:
x = 168 / 28 x = 6
Step 4: Substitute x = 6 into the first equation:
6*6 + y = 30 36 + y = 30 y = 30 - 36 y = -6
So, the solution to the system of equations is x = 6, y = -6.
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