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3 years ago

What is the solution to the system of the equation.Please help me.

Mathematics

1 answer:

inna [77]3 years ago

3 0

Answer:

x=3, y=2

Step-by-step explanation:

since y =2x-4, we name it as equation I

and the second system as equation 2.

we substitute equation 1 into 2 and we have;

4x+3(2x-4)=18

4x+6x-12=18

10x=18+12

x= 30÷10

x=3.

now, substituting x=3 into the y equation , we have

y= 2(3)-4

y=2.

therefore, x=3, y=2.

...if I was to plot this I would use the equation intercepts. Some people might use the slope whichever is okay for you. but I like to use the intercepts...(x,y)

so first, to find the intercept of equation 1;

we have,

y=2x-4

we set x= 0 and we get .y=2(0)-4=-4, we have (0,-4)...x=0, y=-4 for intercept

we set y to 0 to get the intercept for x...

we have, 0=2x-4=2..we get (2,0)...x=2, y=0 for the second intercept.

we do same for the second equation...

4x+3y=18...

so when doing this set x to 0 to get y intercept that is (0,y) and set y= 0 to get the x intercept that is (x,0)... then you can plot the points on your graph...

the intercept of the two system after you've plotted it on your graph should give you the solution we have that is x=3, y=2.

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3 years ago

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Anvisha [2.4K]

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2 years ago

What is the equation for the linear model in the scatter plot obtained by choosing the two points closest to the line?

HACTEHA [7]

Answer:

Option C is the answer.

Step-by-step explanation:

To find the equation of the straight line equation i.e, we must be given with the two points $\left (x_{1},y_{1} \right )$ and $\left (x_{2},y_{2}\right )$

Since from the graph the two points closest to the line are $\left ( 10,36 \right )$ and $\left ( 22,12 \right ).$

Equation of line with two points closest to the line :

$y-y_{1}=m\cdot \left ( x-x_{1} \right )$

where m is the slope.

First we find the slope(m)= $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{12-36}{22-10}$

on simplify we get, $m=-2$ .

Now, to find the equation of the line: $y-y_{1}=m\cdot \left ( x-x_{1} \right )$

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Apply distributive property on right hand side, we get

$y-36=-2\cdot x+20$

Adding both sides by 36, we get

$y=-2x+20+36$

$y=-2x+56$ .

The equation for the linear model in the scatter plot obtained by the two closest point $\left ( 10,36 \right ) and \left ( 22,12 \right )$ closest to the line is,