Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Use the diagram to work out the solution to these simultaneous equations:

[tex]\[
\begin{array}{c}
y - 2x = 8 \\
2x + 5y = 16
\end{array}
\][/tex]


Sagot :

To solve the system of simultaneous equations:

[tex]\[ \begin{array}{c} y - 2x = 8 \\ 2x + 5y = 16 \end{array} \][/tex]

we can use the method of substitution or elimination. Here, we'll demonstrate the substitution method for clarity.

1. Solve the first equation for [tex]\( y \)[/tex]:

[tex]\[ y - 2x = 8 \][/tex]

Add [tex]\( 2x \)[/tex] to both sides:

[tex]\[ y = 2x + 8 \][/tex]

2. Substitute this expression for [tex]\( y \)[/tex] into the second equation:

[tex]\[ 2x + 5(2x + 8) = 16 \][/tex]

3. Expand and simplify the equation:

[tex]\[ 2x + 10x + 40 = 16 \][/tex]

Combine like terms:

[tex]\[ 12x + 40 = 16 \][/tex]

4. Isolate [tex]\( x \)[/tex]:

Subtract 40 from both sides:

[tex]\[ 12x = 16 - 40 \][/tex]

[tex]\[ 12x = -24 \][/tex]

Divide both sides by 12:

[tex]\[ x = -2 \][/tex]

5. Substitute [tex]\( x = -2 \)[/tex] back into the expression for [tex]\( y \)[/tex]:

[tex]\[ y = 2(-2) + 8 \][/tex]

[tex]\[ y = -4 + 8 \][/tex]

[tex]\[ y = 4 \][/tex]

Thus, the solution to the system of equations is:

[tex]\[ \boxed{x = -2 \quad \text{and} \quad y = 4} \][/tex]