Question

How do you solve the system of equations: \[4x + 3y = 7\] and \[ - 2x + y = 9\]?

Answer 1

Hint: In the given question, we have been given that there are two linear equations. The two equations are linear equations in two variables. We have to solve them. Solving them means to calculate the value of the two variables. To do that, we are going to make the coefficient of any one variable in the equations equal, then subtract them and they become zero (because they are equal), then we get one equation in only one variable. Then simply find the value of the variable, put it in any one equation and find the value of the second variable.

Complete step by step solution:
The given equations are:
\[4x + 3y = 7\]
\[ - 2x + y = 9\]
Multiplying the second equation by \[2\],
\[ - 4x + 2y = 18\]
Now, adding the two equations,
\[{\rm{ }}4x + 3y = 7\]
\[ - 4x + 2y = 18\]
\[5y = 25\]
Hence, \[y = 5\].
Now, putting \[y = 5\] in the second equation,
\[ - 2x + 5 = 9 \Rightarrow - 2x = 4\]
Hence, \[x = - 2\].

Note: In the given question, we were given two linear equations in two variables. We had to find the value of the variables. We did that by making one variable in both the equations equal by multiplying with appropriate constant. Then we subtract the two equations, and the chosen variable is removed from the equation as we subtracted two equals. Then we found the value of the other variable. After that, we put the calculated value of the variable into any one equation and found the value of the second variable.