18. Systems of Equations and Matrices

Two Variable Systems of Linear Equations

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Use the elimination method to solve the following system of linear equations.
$2x+y=1$
$3x-y=4$

$\left(-1,1\right)$

$\left(1,1\right)$

$\left(1,-1\right)$

$\left(-1,-1\right)$

Verified step by step guidance

First, write down the system of equations: 2x + y = 1 and 3x - y = 4.

To use the elimination method, add the two equations together to eliminate y. This is possible because the coefficients of y are +1 and -1.

Add the equations: (2x + y) + (3x - y) = 1 + 4. This simplifies to 5x = 5.

Solve for x by dividing both sides of the equation by 5, resulting in x = 1.

Substitute x = 1 back into one of the original equations, for example, 2x + y = 1, to find y. This gives 2(1) + y = 1, which simplifies to y = -1.

Master Introduction to Systems of Linear Equations with a bite sized video explanation from Patrick

Problem sets built by lead tutors

Expert video explanations

Use the elimination method to solve the following system of linear equations.2x+y=12x+y=12x+y=13x−y=43x-y=43x−y=4