Question

How do you solve the system of equations $5x-y=-26$ and $-4x-6y=1.4$ ?

Answer 1

Hint: In this question, we have to find the value of x and y. Thus, we will use the substitution method to get the solution. First, we will subtract 5x on both sides and then we will multiply (-1) on both sides to get a new equation of y in terms of x. After that, we will substitute the value of y in the second equation and solve for x. In the last, we will put the value of x in the equation of y, to get the required solution for the problem.

Complete step by step answer:
According to the problem, we have to find the value of x and y.
Thus, we will use the substitution method to get the solution.
The equations given to us are $5x-y=-26$ -------- (1) and $-4x-6y=1.4$ ------ (2)
Now, we will first solve equation (1), that is subtract 5x on both sides in the same equation, we get
$\Rightarrow 5x-y-5x=-26-5x$
As we know, the same terms with opposite signs cancel out each other, thus we get
$\Rightarrow -y=-26-5x$
Now, we will multiply (-1) on both sides in the above equation, we get
$\Rightarrow -y.\left( -1 \right)=\left( -26-5x \right).\left( -1 \right)$
On further solving, we get
$\Rightarrow y=26+5x$ ------ (3)
Now, we will substitute the value of equation (3) in equation (2), we get
$\Rightarrow -4x-6\left( 26+5x \right)=1.4$
Now, we will apply the distributive property $a\left( b+c \right)=ab+ac$ in the above equation, we get
$\Rightarrow -4x-6\left( 26 \right)-6\left( 5x \right)=1.4$
On further solving, we get
$\Rightarrow -4x-156-30x=1.4$
$\Rightarrow -34x-156=1.4$
Now, we will add 156 on both sides in the above equation, we get
$\Rightarrow -34x-156+156=1.4+156$
As we know, the same terms with opposite signs cancel out each other, thus we get
$\Rightarrow -34x=157.4$
Now, we will divide (-34) on both sides in the above equation, we get
 $\Rightarrow \left( \dfrac{-34}{-34} \right)x=\dfrac{157.4}{-34}$
Thus, we get
$\Rightarrow x=-\dfrac{787}{170}$ ------- (4)
Now, we will substitute the value of equation (4) in equation (3), we get
$\Rightarrow y=26+5\left( \dfrac{-787}{170} \right)$
$\Rightarrow y=26-\dfrac{787}{34}$
On taking the LCM of the denominator in the above equation, we get
$\Rightarrow y=\dfrac{884-787}{34}$
Therefore, we get
$\Rightarrow y=\dfrac{97}{34}$

Therefore, for the equations $5x-y=-26$ and $-4x-6y=1.4$, the value of x and y are $-\dfrac{787}{170}$ and $\dfrac{97}{34}$ respectively.

Note: While solving this problem, do mention all the steps properly to avoid confusion and mathematical error. You can also solve this problem, using cross multiplication or the elimination method to get the solution.