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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 :

GinnyAnswer
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]
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