Final answer:
To solve the system of equations 4x + 8y = 4 and 2x – 7y = -11, combine the equations by eliminating one variable. After eliminating y, solve for x and substitute the value of x to solve for y.
Step-by-step explanation:
To solve the system of equations 4x + 8y = 4 and 2x – 7y = -11, we can use the method of combining equations. First, we need to eliminate one variable, either x or y, by multiplying one or both equations by appropriate constants. In this case, we'll eliminate y. Multiply the first equation by -7 and the second equation by 8. This gives us -28x - 56y = -28 and 16x - 56y = -88. Now, add the two equations together to eliminate y: -28x - 56y + 16x - 56y = -28 - 88. Simplify the equation: -12x = -116. Divide both sides by -12 to solve for x: x = 9⁄3 = 3. Substitute the value of x into one of the original equations to solve for y. Using the first equation, we have 4(3) + 8y = 4. Simplify the equation: 12 + 8y = 4. Subtract 12 from both sides: 8y = -8. Divide both sides by 8 to solve for y: y = -1.