Question

Solve the following system of equations using the method of vour choice.- 2x + 5y- - 3x + 4y = 21

Answer 1

`\begin{gathered} x=9 \\ y=3 \end{gathered}`

Step-by-step explanation:

Step 1. The system of equations given is:

`\begin{gathered} -2x+5y=-3 \\ x+4y=21 \end{gathered}`

And we are required to find the solution to the system, which is to find the value of x and y.

Step 2. We will solve this system of equations using the elimination method. The method consists of modifying one or the two equations such that when we add them, one of the variables is eliminated.

For this reason, to eliminate the x variable, we will multiply the second equation by 2:

`2(x+4y=21)\longrightarrow\boxed{2x+8y=42}`

Step 3. Add the first equation of the system, and the boxed equation from step 2:

When we add them, -2x and 2x cancel each other, and the result is:

Step 4. From the resulting equation:

`13y=39`

We solve for y:

`\begin{gathered} y=(39)/(13) \\ \downarrow\downarrow \\ \boxed{y=3} \end{gathered}`

Step 5. Using the value of y, and substituting it into any equation from the system we will find the value of x.

Substituting y=3 into the following equation:

`\begin{gathered} x+4y=21 \\ \text{substituting y=3} \\ x+4(3)=21 \\ \text{solving for x:} \\ x+12=21 \\ x=21-12 \\ \boxed{x=9} \end{gathered}`

Answer:

`\begin{gathered} x=9 \\ y=3 \end{gathered}`