Solve x_{1} + x_{2} = 22; x_{1} + x_{3} = 19 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$x_{1}+x_{2}=22; x_{1}+x_{3}=19$$

Solve for x_1, x_2

$x_{1}=19-x_{3}$
$x_{2}=x_{3}+3$

Steps Using Substitution

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$$x_{1}+x_{3}=19,x_{1}+x_{2}=22$$

Pick one of the two equations which is more simple to solve for $x_{1}$ by isolating $x_{1}$ on the left hand side of the equal sign.

$$x_{1}+x_{3}=19$$

Subtract $x_{3}$ from both sides of the equation.

$$x_{1}=19-x_{3}$$

Substitute $19-x_{3}$ for $x_{1}$ in the other equation, $x_{1}+x_{2}=22$.

$$19-x_{3}+x_{2}=22$$

Subtract $19-x_{3}$ from both sides of the equation.

$$x_{2}=x_{3}+3$$

The system is now solved.

$$x_{1}=19-x_{3},x_{2}=x_{3}+3$$