Solve the system of equations by any method

3x + 5y = 21
2x - y = 1

x = 2

y = 3

Step-by-step explanation:

Solving by substitution:

3x + 5y = 21

2x - y = 1

2x - y = 1 → -y = -2x + 1 → y = 2x - 1.

y = 2x - 1 → 3x + 5y = 21 → 3x + 5(2x - 1) = 21 →

3x + 5(2x) + 5(-1) = 21 → 3x + 10x - 5 = 21 →

3x + 10x = 26 → 13x = 26 → 13x/13 = 26/13 →

x = 2.

x = 2 → y = 2x - 1 → y = 2(2) - 1 → y = 4 - 1 →

y = 3.

Verify:

3x + 5y = 21 → 3(2) + 5(3) = 21 → 6 + 15 = 21 → 21 = 21.

2x - y = 1 → 2(2) - (3) = 1 → 4 - 3 = 1 → 1 = 1.

Solve by graphing:

Given two linear equations making up a system in the standard form Ax + By = C.

It is easiest to graph by setting the x to zero to find the y intercept, and the y to zero to find the x intercept, and then finding the slope using m = -A/B → ∆y/∆x.

And connecting the two intercepts to form that line.

This slope is the steepness of the line or the rise in y units over the run in x units, represented by the change in y over the change in x.

The solution of this linear system is where the two lines intersect.

Once you graph these two lines, you will realise that they intersect at the point (2,3) where a coordinate is in the form (x,y) meaning that x is 2, and y is 3 when they intersect.

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