Question

How do you solve the system of equations `y+ 3= 2x` and `y + 4= 3x`?

Answer 1

`x=1,y=-1`

Explanation:

Equation 1: `y+3=2x`
Equation 2: `y+4=3x`

Isolate the variable `y` in equation 1, then plug that into equation 2.
`\color(red)(y=2x-3)`
`\color(red)(y)+4=3x\rarr(\color(red)(2x-3))+4=3x`

Now simplify (add like terms, then solve for `x`)
`2x+1=3x`
`\color(blue)(1=x)`

Plug the value of `x` back into equation 1.
`y+3=2\color(blue)(x)\rarry+3=2(\color(blue)(1))`

Simplify to solve for `y`
`y=-1`

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Checking your answers
Plug the values into either one of the original equations to see if they are true.
Equation 1: `(\color(red)(-1))+3\stackrel(?)(=)2(\color(blue)(1))` becomes `2=2`, so correct
Equation 2: `(\color(red)(-1))+4\stackrel(?)(=)3(\color(blue)(1))` becomes `3=3`, so correct