Solve the following system using the elimination method:
-6x + 2y = 5
12x - 4y = -20
m1 = -A/B = 6/2 = 3.
m2 = -12/-4 = 3.
The Eqs have equal slopes. Therefore, they are parallel and do not intersect.
So there are NO solutions.
Solve the system using the elimination method:
-2x+8y=-20
3x+8y=-12
To solve the system of equations using the elimination method, we want to eliminate one of the variables by manipulating the equations in a way that will result in an equation with only one variable. Here's how you can do it:
Step 1: Multiply the first equation by 2 and the second equation by -1 to make the x-coefficients of the two equations equal.
-6x + 2y = 5 becomes: -12x + 4y = 10
12x - 4y = -20 becomes: -12x + 4y = 20
Step 2: Add the two equations together to eliminate the x variable.
(-12x + 4y) + (-12x + 4y) = 10 + 20
-24x + 8y = 30
Step 3: Simplify the equation further if possible.
-24x + 8y = 30 can be divided by 2 to simplify it:
-12x + 4y = 15
Now, we have a new equation:
-12x + 4y = 15
Step 4: Solve the new equation.
Now, we have a single equation that involves only the variables x and y. To solve for x or y, we need to isolate one of them. Let's isolate x for this example:
-12x + 4y = 15
To isolate x, we need to get rid of the 4y term:
-12x = 15 - 4y
Step 5: Simplify the equation further if possible.
We have isolated x, but you can simplify the equation if needed.
Step 6: Solve for x.
To find the value of x, you would need to know the value of y. The system of equations you provided does not have a unique solution because the equation is dependent on the value of y. Therefore, we cannot find a specific solution using the elimination method alone.
However, if you have additional information or constraints, such as another equation or an inequality, we may be able to find a solution.