Which graph represents the solution set for the system 6x + y > -3 and 2x + y ≤ 4?
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<h2><u>1. Determining the value of x and y:</u></h2>
Given equation(s):
To determine the point of intersection given by the two equations, it is required to know the x-value and the y-value of both equations. We can solve for the x and y variables through two methods.
<h3 /><h3><u>Method-1: Substitution method</u></h3>Given value of the y-variable: 3x - 1
Substitute the given value of the y-variable into the second equation to determine the value of the x-variable.
Combine like terms as needed;
Add 1 to both sides of the equation;
Divide 6 to both sides of the equation;
Now, substitute the value of the x-variable into the expression that is equivalent to the y-variable.
Therefore, the value(s) of the x-variable and the y-variable are;
Convert the equations into slope intercept form;
Clearly, we can see that "y" is isolated in both equations. Therefore, we can subtract the second equation from the first equation.
Now, we can cancel the "y-variable" as y - y is 0 and combine the equations into one equation by adding 3x to 3x and 7 to -1.
This problem is now an algebraic problem. Isolate "x" to determine its value.
Like done in method 1, substitute the value of x into the first equation to determine the value of y.
Therefore, the value(s) of the x-variable and the y-variable are;
The point on a coordinate plane is expressed as (x, y). Simply substitute the values of x and y to determine the intersection point given by the equations.
⇒ (x, y) ⇒ (-1, -4)
Therefore, the point of intersection is (-1, -4).
<h3>Graph:</h3>