A system of linear equation is defined as the set of linear equations with same variables. Using this system of linear equation we can find the value of the variables in the linear equations.This is called as solve for x and y. It can be done by two methods, elimination method and substitution method.
There are calculators to solve for x and y in a system of linear equations. This calculators help to find the value of x and y in a system of linear equations in a fraction of time. Here we will see the principle behind the calculators used to solve for x and y.
Solve for X and Y Calculator
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If we want to solve for x and y in a system of linear equations using a calculator, we have to give the input values to the calculator.
For example, we want to solve for x and y in 2x + 3y = 12
3x - 4y = 1
solve for x and y calculator
The above diagram represents a typical online calculator used to solve for x and y.
We have to enter the coefficients of the variables of the equations.
In the given set of equations,
a = 2, b = 3 and c = 12 for equation 1and
a = 3, b = -4 and c = 1
After entering the values, click the ENTER button.
solve for x and y calculator
After that, we get the results as,
solve for x and y calculator
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Example Problem to Solve for X and Y
Example problem
Solve for x and y in the following equations by elimination method.
4x + 8y = 12 and -4x + 2y = 18
Solution
Let, 4x + 8y = 12 -----------> (1)
-4x + 2y = 18 -----------> (2)
Add both equations,
4x + 8y - 4x + 2y = 12 + 18
10y = 30
Divide by 10 on both sides,
y = 3
Plug y = 3 in equation (1)
4x + 8(3) = 12
4x + 24 = 12
subtract 24 on both sides,
4x = 12 - 24
4x = -12
divide by 4 on both sides,
x = `-12/4`
x = -3
So, x = -3 and y = 3 are the solution for the given equations.
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