Question

find the solution of the system of equations.

10x + 10y = 40

5x + 3y = 8

Explanation:

Step1: Simplify the first equation

Divide the first equation \(10x + 10y = 40\) by 10, we get \(x + y = 4\), which can be rewritten as \(x = 4 - y\).

Step2: Substitute into the second equation

Substitute \(x = 4 - y\) into the second equation \(5x + 3y = 8\). So we have \(5(4 - y) + 3y = 8\).

Step3: Solve for y

Expand the left - hand side: \(20-5y + 3y=8\). Combine like terms: \(20 - 2y=8\). Subtract 20 from both sides: \(-2y=8 - 20=-12\). Divide both sides by - 2: \(y = 6\).

Step4: Solve for x

Substitute \(y = 6\) into \(x = 4 - y\), we get \(x=4 - 6=-2\).

Answer:

The solution of the system of equations is \(x=-2,y = 6\)