Solve the simultaneous equations below using substitution.
\[
\begin{aligned}
y & =10 x+4 \\
2 y+5 x & =13
\end{aligned}
\]
Give your answers as integers or decimals.

Answer

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Answer

\(\boxed{x = 0.2, y = 6}\)

Steps

Step 1 ：Substitute the expression for y from the first equation into the second equation: \(2(10x + 4) + 5x = 13\)

Step 2 ：Simplify the equation: \(20x + 8 + 5x = 13\)

Step 3 ：Combine like terms: \(25x + 8 = 13\)

Step 4 ：Solve for x: \(25x = 5\) and \(x = \frac{1}{5}\)

Step 5 ：Substitute the value of x back into the first equation to find the value of y: \(y = 10(\frac{1}{5}) + 4\)

Step 6 ：Simplify the equation: \(y = 2 + 4\)

Step 7 ：Solve for y: \(y = 6\)

Step 8 ：\(\boxed{x = 0.2, y = 6}\)