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{:[y=-2x+19],[-2x+4y=16]:}

y=−2x+19−2x+4y=16 \begin{array}{l}y=-2 x+19 \\ -2 x+4 y=16\end{array}

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Domain and range of absolute value functions: equationsright chevron icon

Full solution

Q. y=−2x+19−2x+4y=16 \begin{array}{l}y=-2 x+19 \\ -2 x+4 y=16\end{array}
  1. Label Equations: Let's label the equations for convenience:\newlineEquation 11: y=−2x+19y = -2x + 19\newlineEquation 22: −2x+4y=16-2x + 4y = 16
  2. Substitute yy into Equation 22: Substitute yy from Equation 11 into Equation 22:\newline−2x+4(−2x+19)=16-2x + 4(-2x + 19) = 16
  3. Distribute and Simplify: Distribute the 44 into the parentheses: −2x+(−8x+76)=16-2x + (-8x + 76) = 16
  4. Combine Like Terms: Combine like terms: −10x+76=16-10x + 76 = 16
  5. Subtract 7676: Subtract 7676 from both sides:\newline−10x=16−76-10x = 16 - 76
  6. Calculate Right Side: Calculate the right side:\newline−10x=−60-10x = -60
  7. Divide to Solve for xx: Divide both sides by −10-10 to solve for xx:x=−60−10x = \frac{-60}{-10}
  8. Calculate x: Calculate the value of x:\newlinex=6x = 6
  9. Substitute xx into Equation 11: Now, substitute xx back into Equation 11 to find yy:y=−2(6)+19y = -2(6) + 19
  10. Calculate y: Calculate the value of y:\newliney=−12+19y = -12 + 19
  11. Add to Find y: Add the numbers to find yy:y=7y = 7

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