Question

RizerMix · Accepted Answer

To solve the system of equations under the elimination method, we want to eliminate one of the variables in two of the equations by adding or subtracting them. Let's rearrange the equations to have them in standard form first:
$5 x + 4 y - 2 x - 3 y = 4$
$x + y + z = 4$

Next, we can combine like terms in the first equation to get:
$3 x + y = 4$
$x + y + z = 4$

Now we have two equations with two variables. To eliminate y, we can subtract the first equation from the second:
$x + y + z - (3 x + y) = 4 - 4$
$- x + z = 0$

Thus, we have eliminated y and obtained an equation in terms of x and z. To solve for z, we can rearrange the equation:
$- x + z = 0$
$z = x$

Finally, we can substitute this expression for z into one of the original equations, say the second equation, and solve for y:
$x + y + z = 4$
$x + y + x = 4$
$2 x + y = 4$
$y = 4 - 2 x$

Therefore, the solution to the system of equations is:
$x = x$
$y = 4 - 2 x$
$z = x$

We can check that this solution satisfies both equations.

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