Question

Please help me with this question am trying to help my son to understand this better. I have attached an image.Solve the system of equations using the linear combination method.{4x−3y=12 7x−3y=3} Enter your answers in the boxes.x = ___y = ___

Answer 1

ANSWER

$x=-3;y=-8$

EXPLANATION

We want to solve the system of equations using the linear combination method:

$\begin{gathered} 4x-3y=12 \\ 7x-3y=3 \end{gathered}$

This method involves the combination of the two equations to form one simplified equation with only one variable.

From the given equations, we see that the coefficients of y in both equations are equal. Hence, we can combine them by finding the difference between the two equations.

Let us subtract the first equation from the second equation:

$\begin{gathered} 7x-4x-3y-(-3y)=3-12 \\ \Rightarrow3x-3y+3y=-9 \\ 3x=-9 \end{gathered}$

Now, simplify by dividing both sides by 3:

$\begin{gathered} \frac{3x}{3}=-\frac{9}{3} \\ x=-3 \end{gathered}$

To find the value of y, substitute the value of x into the first equation and solve for y:

$\begin{gathered} 4(-3)-3y=12 \\ -12-3y=12 \\ -3y=12+12=24 \\ \Rightarrow y=\frac{24}{-3} \\ y=-8 \end{gathered}$

Hence, the solution to the system of equations is:

$x=-3;y=-8$