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Question: How do you solve \(3x-10y=-25\) and \(4x+40y=20\) ?...

How do you solve 3x−10y=−253x-10y=-25 and 4x+40y=204x+40y=20 ?

Explanation

Solution

We are asked to solve the equation 3x−10y=−253x-10y=-25 and 4x+40y=204x+40y=20 . To do so, we first learn what type of equation we have, what is called a solution, then we look at the possible way to solve our problem, we will use the elimination method to solve for the value of x and y, we will use graphical methods to understand the solution by more than 1 method.

Complete step by step solution:
We are given an equation as 3x−10y=−253x-10y=-25 and 4x+40y=204x+40y=20 .
So, it is a linear equation in two variables.
We have to find the solution of these two equations.
We know that to find the solution of linear equation in two variables, these are various ways like –
1, Elimination method.
2, Substitution method.
3, Cross multiplication method.
4, Graphical method.
To find the solution we can use any of the following and by each method we will always arises at the same

We will use elimination method in this, we will eliminate any one of the variables and then solve for the remaining variable.
To eliminate any variable, we will make their coefficient equal by multiplying the equation with the appropriate constant and then we add or subtract as required to eliminate. Once a variable is eliminated then we solve for another variable.
Now we have 3x−10y=−253x-10y=-25 and 4x+40y=204x+40y=20 .
We can see that the coefficient of ‘y’ in the first equation is -10 and the coefficient of ‘y’ in the 2nd equation is 40.
So, we will multiply equation 1 by 4.
12x−40y=−10012x-40y=-100 .
Now we add 12x−40y=−10012x-40y=-100 with 4x+40y=204x+40y=20 .So,
12x−40y=−100  4x+40y= 20 16x =−80 \begin{aligned} & 12x-40y=-100 \\\ & \text{ }4x+40y=\text{ }20 \\\ & 16x\text{ }=-80 \\\ \end{aligned}
Now solving for ‘x’, we get –
⇒x=−8016\Rightarrow x=\dfrac{-80}{16}
So,
⇒x=−5\Rightarrow x=-5
So, the value of ‘x’ is -5.
Now, we put x=−5x=-5 in equation (1) 3x−10y=−253x-10y=-25 we get –
3(−5)−10y=−253\left( -5 \right)-10y=-25
Solving, we get –
−15−10y=−25-15-10y=-25
By solving for ‘y’, we get –
⇒−10y=−25+15 y=1 \begin{aligned} & \Rightarrow -10y=-25+15 \\\ & y=1 \\\ \end{aligned}
So, we get a solution as x=−5x=-5 and y=1y=1 .

Note: To verify our answer, we put x=−5x=-5 and y=1y=1 in another equation 4x+40y=204x+40y=20 .
We put x=−5x=-5 and y=1y=1 , we get –

& \Rightarrow 4\left( -5 \right)+40\left( 1 \right)=20 \\\ & -20+40=20 \\\ \end{aligned}$$ By solving, we get – $20=20$ Which is true. So, $x=-5,y=1$ is the correct solution. We can also graph these equations, the point where these two equations will last each other on the graph. That point will be the solution to our given problem.