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{:[3a+5u=17],[2a+u=9]:}

{:\begin{align}[ $3$ a+ $5$ u&= $17$ ],[ $2$ a+u&= $9$ ]:\end{align}

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Write an equation word problem

Full solution

Q. {:\begin{align*}[

3

a+

5

u&=

17

],[

2

a+u&=

9

]:\end{align*}

Solve for 'u': Step $1$ : Solve the second equation for 'u'. $\newline$ Given: $2a + u = 9$ $\newline$ Subtract $2a$ from both sides: $u = 9 - 2a$
Substitute into first equation: Step $2$ : Substitute the expression for $u$ from Step $1$ into the first equation. $\newline$ Substitute $u = 9 - 2a$ into $3a + 5u = 17$ : $\newline$ $3a + 5(9 - 2a) = 17$
Simplify and solve for 'a': Step $3$ : Simplify and solve for 'a'. $\newline$ $3a + 45 - 10a = 17$ $\newline$ $-7a + 45 = 17$ $\newline$ Subtract $45$ from both sides: $-7a = -28$ $\newline$ Divide by $-7$ : $a = 4$
Substitute back for 'u': Step $4$ : Substitute the value of 'a' back into the expression for 'u' to find 'u'. $\newline$ $u = 9 - 2(4)$ $\newline$ $u = 9 - 8$ $\newline$ $u = 1$

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