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Solve the system of equations using SUBSTITUTION. {:[y=2x+5],[y=x+7]:}

Solve the system of equations using SUBSTITUTION.\newliney=2x+5y=x+7 \begin{array}{l} y=2 x+5 \\ y=x+7 \end{array}

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Full solution

Q. Solve the system of equations using SUBSTITUTION.\newliney=2x+5y=x+7 \begin{array}{l} y=2 x+5 \\ y=x+7 \end{array}
  1. Set Equations Equal: Since both equations are equal to yy, we can set them equal to each other: 2x+5=x+72x + 5 = x + 7.
  2. Isolate Terms with x: Subtract xx from both sides to isolate terms with xx on one side: 2x−x+5=72x - x + 5 = 7.
  3. Combine Like Terms: Simplify the equation by combining like terms: x+5=7x + 5 = 7.
  4. Solve for x: Subtract 55 from both sides to solve for x: x=7−5x = 7 - 5.
  5. Calculate x Value: Calculate the value of x: x=2x = 2.
  6. Substitute xx Value: Substitute x=2x = 2 into one of the original equations to find yy. We'll use y=2x+5y = 2x + 5: y=2(2)+5y = 2(2) + 5.
  7. Calculate y Value: Calculate the value of y: y=4+5y = 4 + 5.
  8. Simplify to Find y: Simplify to find the value of yy: y=9y = 9.

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