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sergey [27]
4 years ago
9

Solve the system of equations. {y=x^2+9 {y=6x

Mathematics
1 answer:
adoni [48]4 years ago
6 0
<span><span> {y,x} = {7,2}</span>  </span>System of Linear Equations entered :<span><span>  [1] y - 6x = -5 </span><span>  [2] y + x = 9 </span></span>Graphic Representation of the Equations :<span> -6x + y = -5 x + y = 9
</span>
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y = \frac{7}{9} x+\frac{17}{9}

Step-by-step explanation:

1) First, find the slope of the line. Use the slope formula, m = \frac{y_2-y_1}{x_2-x_1}. Substitute the x and y values of the given points into the formula and solve:

m = \frac{(5)-(-2)}{(4)-(-5)} \\m  = \frac{5+2}{4+5} \\m = \frac{7}{9}

So, the slope is \frac{7}{9}.

2) Now, use the point-slope formula y-y_1 = m (x-x_1) to write the equation of the line. Substitute m, x_1, and y_1 for real values.

Since m represents the slope, substitute \frac{7}{9} for it. Since x_1 and y_1 represent the x and y values of one point the line intersects, choose from any one of the given points (it doesn't matter which one, either way the result equals the same thing) and substitute its x and y values into the formula as well. (I chose (4,5), as seen below.) From there, isolate y to place the equation in slope-intercept form (y = mx + b format) and find the following answer:

y-(5) = \frac{7}{9} (x-(4))\\y-5 = \frac{7}{9} (x-4)\\y -5=\frac{7}{9} x-\frac{28}{9}\\y = \frac{7}{9}  x-\frac{28}{9} +\frac{45}{9}\\y = \frac{7}{9} x+\frac{17}{9}

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