graph and check to solve the linear system. problem: 2x-3y=-3
x+6y=6
You know it is impossible to graph anything using a keyboard.
Do this:
1-Isolate y for both equations.
2-Select about 3 values for x and solve for y in both equations.
3-Then graph the points that you find on the xy-plane.
4-Connect the points with a solid line.
5-The solution of this system of linear equations in two variable will be where the two graphs meet or cross each other on the xy-plane.
Got it?
4.8*10^-9 =x^2/.350
To graph and check the solution of the linear system, we first need to solve it. Let's solve the given system of equations step by step.
Step 1: Solve the first equation, 2x - 3y = -3, for x.
2x - 3y = -3
2x = 3y - 3
x = (3y - 3) / 2
Step 2: Solve the second equation, x + 6y = 6, for x.
x + 6y = 6
x = 6 - 6y
Now we have expressed both x and y in terms of the other variable.
Step 3: Substitute the value of x (from Step 2) into the first equation.
(3y - 3) / 2 - 3y = -3
Multiply through by 2 to eliminate the fraction.
3y - 3 - 6y = -6
Combine like terms.
-3y - 3 = -6
Add 3 to both sides.
-3y = -3
Step 4: Solve for y.
-3y = -3
Divide by -3.
y = 1
Step 5: Substitute the value of y (from Step 4) into the second equation.
x + 6(1) = 6
x + 6 = 6
Subtract 6 from both sides.
x = 0
So we have found that the solution to the given linear system of equations is x = 0 and y = 1.
Now, let's graphically check the solution.
To graph the linear system, plot the points (x, y) that satisfy both equations on a coordinate plane. The point where the two lines intersect is the solution to the system.
For the equation 2x - 3y = -3, we can rewrite it in slope-intercept form (y = mx + b) by solving for y:
-3y = -2x - 3
Divide by -3.
y = (2/3)x + 1
For the equation x + 6y = 6:
6y = -x + 6
Divide by 6.
y = (-1/6)x + 1
Now, plot the two lines on a coordinate plane using the slope-intercept form equations.