Question

How do you solve \[2x+9y=17\] and \[x=7-4y\]?

Answer 1

Hint: For the given question we are given to solve the equation \[2x+9y=17\] and \[x=7-4y\]. As we can see that there is no coefficient is common in both equations. So we have to use a substitution method for solving this problem.

Complete step by step solution:
\[2x+9y=17\] and \[x=7-4y\]
Now we have to write both equations as equation(1) and equation (2)
\[2x+9y=17............(1)\]
\[x=7-4y............(2)\]
Here it is given that in equation(2) x coefficient is given so we can find so easily.we have to substitute the given x coefficient in equation(1)
\[\Rightarrow 2(7-4y)+9y=17\]
Now we have multiplied the factors which are below to go to the next step. After multiplying we get
\[\Rightarrow 14-8y+9y=17\]
Now we have to add the factors which are below to go to the next step. After adding we get
\[\Rightarrow 14+y=17\]
Now we have to send the numerical which is present on left hand side to right hand side
\[\Rightarrow y=17-14\]
Now we have to subtract the numerical which is present on the right hand side in the equation. After subtraction we get
\[\Rightarrow y=3\]
Now we have to find x coefficient. So we have to substitute \[y=3\] in equation(2)
\[\Rightarrow x=7-4y\]
After substitution we get
\[\Rightarrow x=7-4\left( 3 \right)\]
\[\Rightarrow x=7-12\]
\[\Rightarrow x=-5\]
And now we take \[x=-5\] as equation(3) and \[y=3\] as equation(4)
\[x=-5............(3)\]
\[y=3............(4)\]
Both the above equations are the solutions of the given question

Note: We can do this problem even by substituting the both equations given doesn’t have any common coefficients so we have to use a substitution method for this. To verify our answers we can check by substituting x and y values in the question.