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Sagot :
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].
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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