how do you solve linesr equqtions?

Question

2x+3y=12

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Answer 1

2x + 3y = 12 is the equation of a line in standard form and, since there are an infinite number of points on a line, there are an infinite number of correct solutions.

If you have a second linear equation, then you have 3 possibilities:

1. The second equation is merely a mathematical permutation of the first such as 4x + 6y = 24 and describes the same line, thus again having an infinite number of solutions.
2. The second equation intersects the first in only one point and the solution is the point of intersection. For example, if the 2nd equation was x = 3: 2*3 + 3y = 12 -> 6 + 3y = 12 -> 3y = 6 -> y = 2. Therefore, the solution of that system of equations is (3, 2).
3. The second equation is parallel to the first such as x + 3y = 6. In this case, the two lines never meet and there is no solution.

Answer 2

Cyrstal G. is correct. You should have two equations and then you will be able to solve.

Answer 3

If you are showing the solution by graphing, since it is already in standard form, the easiest and most direct method is using intercepts. It important to know that the value of y at the x-intercept and vice versa.

Given the equation 2x + 3y = 12, if y=0, 2x = 12, so the x-intercept is (6,0). Additionally, of x=12, 3y=12, so the y-intercept is (0,4). Now that you have two points, you can draw a line through them. Any point on that line is a solution of the equation.

From here, you can find the solution of two equations (the intersection point) . There are 3 possibilities, one intersection point if they intersect one point; no intersection point, therefore no solution, if the lines are parallel; or an infinite number of solutions if they are the same line, as in the case of 4x+6y=24 (doubling each term).

Answer 4

Assuming your two equations are 2x+3y=12 and 6x+4y=12 then you would do the following to solve for x and y:

2x+3y=12 & 6x+4y=12

2x+3y=12=6x+4y

2x+3y=6x+4y

subtract 2x from both sides 2x+3y -2x = 6x+4y -2x

3y=4x+4y

subtract 4y from each side 3y -4y= 4x+4y -4y

-y = 4x

multiply each side by negative one (-1)*-y = (-1)*4x

y=-4x

input the y value into the original equation 2x+3(-4x)=12

2x-12x=12

-10x=12

x=-12/10=-6/5=-1.2

now input your x value into the original equation to solve for y

2(-6/5)+3y=12

-(12/5)+3y=12

3y=12+(12/5)=((12*5)/5)+(12/5)=(60/5)+(12/5)=72/5

y=(72/5)/3=72/(3*5)=(72/3)/5=24/5=4.8

x= -6/5        y= 24/5

if you put both the x and y values into the equation 2x+3y or 6x+4y they will both equal 12

 

Answer 5

Does this problem come with a second equation? If there are two variables, you need at least two equations to be able to find the value of each variable.