Can someone help solve this ? Solve the system of equations 2x-y= 13x and -3x+2y=-18 by combining the equations.

x = 18/25, y = -198/25

Step-by-step explanation:

Given the system of equations:

2x – y = 13x

-3x + 2y= -18

You can combine these two equations effectively by multiplying the first equation by 2, and adding because -2y and 2y will cancel out when added. So you will be left with only x terms

( 2x - y = 13x ) × 2

+ -3x + 2y = -18

2(2x) - 3x + 2(-y) + 2y = 2(13x) - 18

4x - 3x - 2y + 2y = 26x - 18

x + 0 = 26x - 18

x = 26x - 18

[Then use the properties of equality to simplify the expressions in the equation to derive the value of x]

x - x = 26x - 18 - x (subtraction property of equality)

0 = 25x - 18

0 + 18 = 25x - 18 + 18 (addition property of equality)

18 = 25x

18 / 25 = 25x / 25 (division property of equality)

18 / 25 = x

x = 18 / 25 (symmetric property of equality)

Now with the value of x, we can find the value of y by substituting the value of x into the variables of the top equation {2x – y = 13x} because this involves the simpliest steps.

Given x = 18 / 25.

2x – y = 13x → 2x – y + y = 13x + y → 2x = 13x + y → 2x – 13x = 13x + y – 13x → -11x = y → y = -11x.

Now that we know y = -11x, y = -11(18/25) which is - (11 × 18) / 25 = -198/25

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be