3.09 Elimination method for simultaneous equations
Interactive practice questions
Given the following equations, we want to solve for $x$x and $y$y using the elimination method.
| Equation 1 | $6x+3y=3$6x+3y=3 |
| Equation 2 | $5x-3y=30$5x−3y=30 |
Notice that Equation 1 has a $3y$3y term and Equation 2 has a $-3y$−3y term. How can we combine the equations to eliminate the $y$y-terms?
Equation 1 $+$+$2\times$2× Equation 2
$2\times$2× Equation 1 $-$− Equation 2
Equation 1 $+$+ Equation 2
Equation 1 $-$− Equation 2
Solve for $x$x by adding Equations 1 and 2 together.
Enter each line of working as an equation.
Substitute $x=3$x=3 into either of the equations and solve for $y$y.
Enter each line of working as an equation.
Given the following equations, we want to solve for $x$x and $y$y using the elimination method.
| Equation 1 | $3x+2y=-3$3x+2y=−3 |
| Equation 2 | $-3x+6y=27$−3x+6y=27 |
Given the following equations, we want to solve for $x$x and $y$y using the elimination method.
| Equation 1 | $8x+3y=-9$8x+3y=−9 |
| Equation 2 | $5x+3y=0$5x+3y=0 |
Given the following equations, we want to solve for $x$x and $y$y using the elimination method.
| Equation 1 | $x+6y=-2$x+6y=−2 |
| Equation 2 | $x+3y=-5$x+3y=−5 |