Question 68733: 1: Plot the graph of the equation 2x-3y=6 and 2x+y=-10 and intercept the result.
2: Plot the graph of the equations 2x+4y=10 and 3x+6y=12 and intercept the result.
3: Determine graphically the vertices of the triangle, the equation of whose sides are given y=x; y=0; 2x+3y=10, interpret the result?
Answer by rmromero(383)   (Show Source):
You can put this solution on YOUR website! 1: Plot the graph of the equation 2x-3y=6 and 2x+y=-10 and intercept the result.
To graph the equations, rewrite the equations written in standard form to slope-intercept form of the equation. y = mx + b
2x-3y=6
3y = 2x + 6
y = 2/3x + 2
2x+y=-10
y = -2x - 10
To solve for the intercept, We will use substitution method.
1. In either equation, solve for one variable in terms of the other.
2x+y=-10
y = -2x - 10
2. Substitute for that variable in the other equation. Solve.
2x-3y=6
2x - 3(-2x-10) = 6
2x + 6x + 30 = 6
8x + 30 = 6
8x = -24
x = -3
3. Substitute the result from step 2 in either equation. Solve for the other variable.
2x+y=-10 , x = -3
2(-3)+y = -10
-6 + y = -10
y = -4
4. Check the solution in both original equations.
2x+y=-10, x = -3, y = -4
2(-3) + (-4) = -10
-6 -4 = -10
-10 = -10 --------->> True
2x-3y=6, x = -3, y = -4
2(-3)-3(-4) = 6
-6 + 12 = 6
6 = 6 ---------->> True
Therefore the lines intersect when x = -3 and y = -4
2: Plot the graph of the equations 2x+4y=10 and 3x+6y=12 and intercept the result.
To graph the equations, rewrite the equations written in standard form to slope-intercept form of the equation. y = mx + b
2x+4y=10
4y = -2x+10
y = (-2/4)x+10/4
y = (-1/2)x+(5/2)
3x+6y=12
6y = -3x+12
y = (-3/6)x+(12/6)
y = (-1/2)x+2
To solve for the intercept, We will use substitution method.
1. In either equation, solve for one variable in terms of the other.
3x+6y=12
6y = -3x+12
y = (-3/6)x+(12/6)
y = (-1/2)x+2
2. Substitute for that variable in the other equation. Solve.
2x+4y=10
2x + 4((-1/2)x+2) = 10
2x + -2x + 8 = 10
8 = 10 ---------->> Not True
Therefore the lines do not have an intersection.
3: Determine graphically the vertices of the triangle, the equation of whose sides are given y=x; y=0; 2x+3y=10, interpret the result?
Graph each equation y=0. Since y=x, then x=0.
To graph 2x+3y =10, we are going find y-intercept and x-intercept
2x+3y=10
To find y-intercept by substituting 0 for x.
2(0) + 3y = 10
3y = 10
y = 10/3 ----->y-intercept (0, 10/3)
To find x-intercept by substituting 0 for y.
2x + 3(0) = 10
2x = 10
x = 5 --------->> x-intercept (5, 0)
Notice that the y-intercept (0, 10/3) is one of the vertex of the triangle. x-intercept (5, 0) is the other vertex of the triangle formed. And lastly, the origin (0,0).
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