y > (1/3)x + 4 has an infinite number of solutions. Draw a dashed line representing y = (1/3)x + 4 and then pick points at random on either side of this line. For example, pick (1, 6). Substitute 1 for x in y > (1/3)x + 4 and 6 for y. Is the resulting inequality true? Is 6 > (1/3)(1) + 4 true? YES. So we know that (1, 6) is a solution of y > (1/3)x + 4. Because (1, 6) lies ABOVE the line y = (1/3)x + 4, we can conclude that all points abovve this line are solutions.

6 0

3 years ago

I need help 6x-2y=10 x-2y=-5 solve by elimination

dem82 [27]

<h3>Explanation</h3>

Given the system of equations.

$\begin{cases} 6x - 2y = 10 \\ x - 2y = - 5 \end{cases}$

Solve the system of equations by eliminating either x-term or y-term. We will eliminate the y-term as it is faster to solve the equation.

To eliminate the y-term, we have to multiply the negative in either the first or second equation so we can get rid of the y-term. I will multiply negative in the second equation.

$\begin{cases} 6x - 2y = 10 \\ - x + 2y = 5 \end{cases}$

There as we can get rid of the y-term by adding both equations.

$(6x - x) + ( - 2y + 2y) = 10 + 5 \\ 5x + 0 = 15 \\ 5x = 15 \\ x = \frac{15}{5} \longrightarrow \frac{ \cancel{15}}{ \cancel{5}} = \frac{3}{1} \\ x = 3$

Hence, the value of x is 3. But we are not finished yet because we need to find the value of y as well. Therefore, we substitute the value of x in any given equations. I will substitute the value of x in the second equation.

$x - 2y = - 5 \\ 3 - 2y = - 5 \\ 3 + 5 = 2y \\ 8 = 2y \\ \frac{8}{2} = y \\ y = \frac{8}{2} \longrightarrow \frac{ \cancel{8}}{ \cancel{2}} = \frac{4}{1} \\ y = 4$

Hence, the value of y is 4. Therefore, we can say that when x = 3, y = 4.

Answer Check by substituting both x and y values in both equations.

First Equation

$6x - 2y = 10 \\ 6(3) - 2(4) = 10 \\ 18 - 8 = 10 \\ 10 = 10 \longrightarrow \sf{true} \: \green{ \checkmark}$

Second Equation

$x - 2y = - 5 \\ 3 - 2(4) = - 5 \\ 3 - 8 = - 5 \\ - 5 = - 5 \longrightarrow \sf{true} \: \green{ \checkmark}$

Hence, both equations are true for x = 3 and y = 4. Therefore, the solution is (3,4)

<h3>Answer</h3>

$\begin{cases} x = 3 \\ y = 4 \end{cases} \\ \sf \underline{Coordinate \: \: Form} \\ (3,4)$

8 0

3 years ago