how to solve questions like x+12+y+22=x+342=0, I like iron man a lot

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Multi-variable equations contain two or more unknown variables that we need to solve for simultaneously. In our example x plus 12 plus y plus 22 equals x plus 342 equals 0, this notation represents a system of connected equations. The equals signs create a chain, meaning the first expression equals the second, and the second equals zero. This gives us two separate equations that must both be true at the same time. To solve this system effectively, we must separate the chain of equations into individual, manageable parts. The original expression x plus 12 plus y plus 22 equals x plus 342 equals 0 contains two equality relationships. We can split this into equation 1: x plus 12 plus y plus 22 equals x plus 342, and equation 2: x plus 342 equals 0. This separation maintains the mathematical integrity because both equations must be satisfied simultaneously for the original statement to be true. When solving multi-variable systems, we start with the simpler equation first. From x plus 342 equals 0, we can easily isolate x by subtracting 342 from both sides, giving us x equals negative 342. Now we have the value of one variable. Next, we substitute this value back into the first equation. Replacing x with negative 342 in the equation x plus 12 plus y plus 22 equals x plus 342, we get negative 342 plus 12 plus y plus 22 equals negative 342 plus 342. This creates a single-variable equation that we can solve for y. Now we substitute x equals negative 342 into our first equation. Starting with negative 342 plus 12 plus y plus 22 equals negative 342 plus 342. First, we simplify the left side: negative 342 plus 12 equals negative 330. The right side: negative 342 plus 342 equals 0. So we have negative 330 plus y plus 22 equals 0. Next, we combine the constants on the left: negative 330 plus 22 equals negative 308. This gives us y plus negative 308 equals 0. Finally, solving for y: y equals 308. Our complete solution is x equals negative 342 and y equals 308. Let's verify our solution x equals negative 342 and y equals 308. Substituting back into the original equation: negative 342 plus 12 plus 308 plus 22 equals negative 342 plus 342 equals 0. Calculating: negative 330 plus 330 equals 0 equals 0. The verification confirms our solution is correct. For similar problems, follow this general strategy: First, separate chain equations into individual equations. Second, solve the simpler equation first. Third, substitute the result into the more complex equation. Fourth, solve for the remaining variable. Finally, always verify your solution by substituting back into the original equation.