Mathematics is a subject that always makes students stressed and frustrated. The formulas used in the subject overwhelmed the many students. Therefore they stuck while solving the maths problems. In this blog, we are providing you with different methods for solving equations easily.
This will help you to get solutions for the equations quickly and effortlessly. Statistics is a science and a practise that uses empirical evidence presented in a quantitative form to improve human understanding. Statistical analysis entails gathering and analysing data, as well as summarising it into numerical form.
The statistics subjects are intertwined. However, if the students do not have a firm grasp of the concepts, the assignment would be difficult for them to complete. As a result, students must need the statistics assignment help in order to submit the best assignment within the defined deadline.The different ways for how to solve the equations in the very simple language provided by us makes you solve the equations easily. We are trying to make maths fun for you.
There are three ways to solve a system of equations-
- Elimination Method
- Substitution Method
- Graphing Method
Elimination Method
- If possible, rearrange both equations so that the x-terms are first, followed by the y-terms, the symbol of equals, and the constant term (in that order). If there seems to be no constant term in an equation, it means the constant term is 0.
- Multiply one (or both) equations by a constant that will cancel either the x-terms or the y-terms when adding or subtracting the equations (when their left sides and their right sides are added separately, or when their left sides and their right sides are subtracted separately).
- Add the calculations or subtract them.
- For the remaining variable, resolve.
- For the other equation, insert the product of step 4 into one of the original equations and solve it.
Example
x + 3y = 12
2x – y = 5
It means that when we use elimination to solve a method, we can get away with one of the variables (eliminate). So we need to substitute or subtract the equations from one another and cancel either the x-terms or the y-terms in this manner.
A good first move will be any of the following options:
- Multiply −2 or 2 from the first equation. In both equations, this will give us 2x or −2x, which would allow the xx-terms to cancel as we add or deduct.
- Multiply 3 or −3 in the second equation. In both equations, this will give us 3y or −3y, which would allow the yy-terms to cancel as we add or subtract.
- Divide by 2 in the second equation. In both equations, this will give us x or −x, which would allow the x-terms to cancel as we add or subtract.
- Divide 3 into the first equation. In both equations, this will give us yy or -y, which would cause the y-terms to cancel as we add or subtract.
Substitution Method
- Have a variable in one of the equations by itself.
- Take the equation you got in step 1 for the variable, and insert it into the other equation (substitute it with square brackets).
- For the remaining variable, solve the equation in step 2.
- Use and insert the outcome from step 3 into the equation from step 1.
Example
x = y+2
3y-2x = 15
- In the second equation, substitute y+2 for x.
3y-2(y+2)= 15
- Distribute the -2 and then merge identical expressions.
3y-2y-4 = 15
y – 4 = 15
- To both sides, add 4
y-4+4=15+4
y=19
- Insert 19 into the first equation for y.
x=y+2
x=19+2
x=21
Solution(21,19)
Graphical Method
- In each equation, solve for Y.
- Graphing all equations on the same system of Cartesian coordinates.
- Find the point of the lines’ intersection point (the point where the lines cross).
Example
x + 3y = 12
2x – y = 5
Let’s place all of them in slope-intercept form to graph these equations. We’re having
x+3y=12
3y=-x+12
y=-1/3x+4
2x-y=5
-y=-2x+5
y=2x-5
- The y-axis at 4 is intersected by the line y=-(1/3)x+4 and then has a slope of -1/3, so its graph is
- The line y= 2x-5 intersects the y-axis at -5 and then has a slope of 2, so you get a graph if you add its graph to the graph of y=-(1/3)x+4
Standing at the point of intersection, it seems as if the solution is roughly (3.75,2.75). The solution is (27/7,19/7)≈(3.86,2.71), so our visual calculation was not too far off (3.75,2.75).
Conclusion
These were the three ways to solve the systems of equations with examples. We have provided you step by step solutions so that it becomes easy for you to understand and solve the question. To become proficient, try to solve more examples and practice daily. As the saying practice makes a man perfect is the best saying for this. The substitution method is the best and easiest method for solving the equations; however, elimination and graphical is also not typical, but the need is to practice. The best method to solve equation is to understand the query first and then start its solution with full concentration and focus.
