Solve the system of equations graphed on the coordinate axes below.y, equals, minus, 3, x, plus, 6y=−3x+6y, equals, start fraction, 2, divided by, 3, end fraction, x, minus, 5y=32 x−5
Question
Solve the system of equations graphed on the coordinate axes below.y, equals, minus, 3, x, plus, 6y=−3x+6y, equals, start fraction, 2, divided by, 3, end fraction, x, minus, 5y=32 x−5
Solution
The system of equations given is:
- y = -3x + 6
- y = 2/3x - 5
To solve this system of equations, we can set the two equations equal to each other because they both equal y:
-3x + 6 = 2/3x - 5
Next, we can solve for x. To do this, we can first get rid of the fraction by multiplying every term by 3:
-9x + 18 = 2x - 15
Then, we can add 9x to both sides to get all x terms on one side:
18 = 11x - 15
Next, add 15 to both sides to isolate the x term:
33 = 11x
Finally, divide both sides by 11 to solve for x:
x = 3
Now that we have x, we can substitute it back into the first equation to solve for y:
y = -3(3) + 6 y = -9 + 6 y = -3
So, the solution to the system of equations is x = 3 and y = -3.
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