Estimate the solution to the system of equations. You can use the interactive graph below to find the solution.

Question

\begin{cases}

-3x+3y=9

\\\\

2x-7y=-14

\end{cases}

Answer 1

There are two ways you could approach this question: elimination or substitution. Elimination involves scaling the equations so that one of the variables cancels when you add the two equations. Substitution involves solving for one of the variables in one equation and plugging it into the second equation. That way one variable can be isolated and solved for and once a value is found you can plug it back into either equation to solve for the other variable. In this case, elimination will be the easiest.

To do so, you will pick a variable and determine what factor to scale each equation by to cancel that variable. For example, if you chose the x-variable, scaling the top equation by +2 would yield

-6x + 6y = 18,

and scaling the bottom equation by +3 would yield

6x -21y = -42.

Adding these equations, the x-variable cancels and you are left with

-15y = -24 and y = 8/5 or 1.6

Then plug this y value into either equation and solve for x.

Answer 2

-3x+3y = 9

2x-7y = -14

graphically 2nd equation is nearly flat, slightly positive slope, 1st equation is diagonal, slope =+1

they intersect in quadrant 2 at (-1.4, 1.6) Use a graphing calculator on line like Desmos, or a handheld calculator like TI83

or solve with algebra

multiply 1st equation by 2, 2nd by 3, then add to eliminate one variable

-6x+6y = 18

6x-21y = -42

-15y = -24

y = -24/-15 = 8/5 = 1.6

2x =7y-14 = 7(8/5)-14

x = 7(4/5)-7 = 28/5 -7

x = (28-35)/5 = -7/5

x =- 1.4

(x,y) = (-1.4, 1.6) = the intersection point of the two lines when the equations are graphed

check the answer, by plugging in the x and y values into the original two given equations:

2x-7y

=2(-1.4) -7(1.6)

=-2.8 - 11.2 = -14

-3x+3y

=-3(-1.4)+3(1.6)

=4.2 + 4.8

= 9

they work, x=-1.4, y=1.6 is the correct answer