Question

What is the solution to the system of equations graphed below?
y = --3/2x+2
y = 5x + 28

Answer 1

(-4, 8) → x = -4 and y = 8

Explanation:

We only need two points to plot the graph of each equation.

`y=-(3)/(2)x+2\\\\for\ x=0\to y=-(3)/(2)(0)+2=0+2=2\to(0,\ 2)\\\\for\ x=2\to y=-(3)/(2)(2)+2=-3+2=-1\to(2,\ -1)\\\\y=5x+28\\\\for\ x=-4\to y=5(-4)+28=-20+28=8\to(-4,\ 8)\\\\for\ x=-6\to y=5(-6)+28=-30+28=-2\to(-6,\ -2)`

Look at the picture.

Read the coordinates of the intersection of the line (solution).

Answer 2

(-4,8)

Explanation:

Given system of equations,

`y=-(3)/(2)x+2-----(1)`

`y=5x+28------(2)`

In equation (1), If x = 0, y = 2,

If y = 0,

`-(3)/(2)x+2=0\implies -(3)/(2)x=-2\implies -3x=-4\implies x=(4)/(3)`

Join the points (0,2) and (4/3,0) in the graph we get the line (1),

In equation (2), if x = 0, y = 28,

If y = 0,

`5x+28=0\implies 5x=-28\implies x=-5.6`

Join the points (0, 28) and (-5.6,0) in the graph we get the line (2),

Hence, by graph,

The intersection point of line (1) and (2) is (-4,8)

Which is the required solution.