Question

How do you solve the system using the elimination method for 2x+3y=7 and 3x+4y=10?

Answer 1

`color(red)("The solution is (2,1).")`

Explanation:

Step 1. Enter the equations.

[1] `2x+3y=7`
[2] `3x+4y=10`

Step 2. Multiply each equation by a number to get the lowest common multiple for the coefficients of one variable.

Multiply Equation 1 by `3` and Equation 2 by `2`.

[3] `6x+9y =21`
[4] `6x+8y=20`

Step 3. Subtract Equation 4 from Equation 3.

[5] `y=1`

Step 4. Substitute Equation 5 in Equation 1.

`2x+3y=7`
`2x+3×1 =7`
`2x+3=7`
`2x=4`

`x=2`

Solution: The solution that satisfies both equations is `(2,1)`.

Check: Substitute the values of `x` and `y` in each Equation.

`2x+3y=7`
`2×2+3×1=7`
`4+3=7`
`7=7`

`3x+4y=10`
`3×2+4×1=10`
`6+4=10`
`10=10`

They check!

Our solution is correct.