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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 :

GinnyAnsweridn
Sure, let's solve this system of equations step-by-step.

The given system of equations is:
[tex]\[ \begin{cases} y - 2x = 8 \\ 2x + 5y = 16 \end{cases} \][/tex]

Step 1: Solve the first equation for \( y \):

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

Add \( 2x \) to both sides:

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

Step 2: Substitute \( y = 2x + 8 \) into the second equation:

The second equation is:

[tex]\[ 2x + 5y = 16 \][/tex]

Substitute \( y \) from step 1:

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

Step 3: Expand and simplify:

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

Combine like terms:

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

Step 4: Solve for \( x \):

Subtract 40 from both sides:

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

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

Divide both sides by 12:

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

Step 5: Substitute \( x = -2 \) back into the expression for \( y \):

We already have \( y = 2x + 8 \):

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

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

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

Solution:

The solution to the system of equations is:

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

So the coordinates [tex]\((x, y)\)[/tex] that satisfy both equations are [tex]\((-2, 4)\)[/tex].
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