Question

How do you solve the system \[x+3y=-4\] and \[2x+6y=5\] by substitution method?

Answer 1

Hint: We can solve this question using basic linear equation concepts. We have to derive x from the given anyone equation. Using that x we will find the value of y by substituting this x in another equation. By simplifying it we will get the value of y . By substituting this y in the first equation we can get x value.

Complete step by step solution:
Given equations are
\[x+3y=-4\]
\[2x+6y=5\]
First we have to find the value of x using any one equation.
We will take the first equation
\[x+3y=-4\]
We have to keep x containing terms on LHS side and remaining terms on RHS side.
So we have to subtract \[3y\] on both sides of the equation.
By subtracting we will get
\[\Rightarrow x+3y-3y=-4-3y\]
By simplifying we will get
\[\Rightarrow x=-4-3y\]
Now we have the x value so we have to substitute this in the second equation.
By substituting the x value in the second equation we will get
\[\Rightarrow 2\left( -4-3y \right)+6y=5\]
Now we have to simplify the equation.
Now we will remove the parenthesis in the equation.
By removing parenthesis we will get
\[\Rightarrow -8-6y+6y=5\]
Now we will further simplify the equation. We will get
\[\Rightarrow -8=5\]

We can see that above equality is false which means that original system has no roots.

Note: We can also solve it by layered method. There we will remain with \[0=-13\] equality which is false. So from this we can say that given equations are two parallel lines. We can draw the graph and we can check our solution.