Question

A system of equations is created by using the line that is created by the equation 3x-2y=-4 and the line that is created by the data in the table below.

x         y
–3    –9
–1    –5
3        3
5        7


What is the y-value of the solution to the system

Answer 1

y=17

Explanation:

Answer 2

Y-value of the solution is 17.

Explanation:

First line of the system of equations is 3x - 2y = (-4) ----(1)

On the basis of given table we will create the equation with the help of the given table.

A line passing through (-3, -9) and (-1, -5)

Slope of the line will be =
`(y-y')/(x-x')`

slope =
`(-5+9)/(-1+3)=(4)/(2)`

slope = 2

Equation of the line may by

y = 2x + c where c is the y- intercept.

This line passes through (3, 3), so putting these values in the equation

3 = 2×3 + c

c = 3 - 6 = -3

Now we are confirm that the equation represented by the table is y = 2x - 3 ------(2)

Now we substitute the value of y from equation 2 to equation 1.

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

3x - 4x + 6 = -4

-x = -10

x = 10

Now we put x = 10 in the equation number 2.

y = 2×10 - 3 = 20 - 3

y = 17

So the solution of the system of the equation is (10, 17)

And the y value of the solution will be 17.