The missing numbers are 18 and -12
Step-by-step explanation:
Let us explain the meaning of coincidental system of equations
- If an equation of a line is ax + by = c, and we multiply or divide all the terms by the same number n, then we will have another equation nax + nby = nc, which represents the same line as the first equation
- The two equations ax + by = c and nax + nby = nc form a coincidental system of two linear equations
- This system has many solutions (all the points on the line)
∵ 2x + 3y = -17 is one equation in a coincidental system of two
linear equations
- To find the other equation multiply each term by n
∴ The second equation is 2nx + 3ny = -17n
∵ The other equation is _y = _x - 102
∵ The other equation is 2nx + 3ny = -17n
- Compare them to equate the like terms
- Subtract both sides by 2nx to have the same form of the other
equation
∴ 3ny = -2nx - 17n
- Equate the numerical terms
∴ -17n = -102
- Divide both sides by -17
∴ n = 6
- Substitute the value of n in the other equation
∴ 3(6)y = -2(6)x - 17(6)
∴ 18y = -12x - 102
∴ The other equation is 18y = -12x - 102
The missing numbers are 18 and -12
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
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