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2 years ago

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What is the solution of the system of equations? {13x−6y=2 3x−4y=−10

1 answer:

Galina-37 [17]2 years ago

3 0

Solve the following system:
{13 x - 6 y = 2 | (equation 1)
{3 x - 4 y = -10 | (equation 2)

Subtract 3/13 × (equation 1) from equation 2:
{13 x - 6 y = 2 | (equation 1)
{0 x - (34 y)/13 = (-136)/13 | (equation 2)

Multiply equation 2 by -13/34:
{13 x - 6 y = 2 | (equation 1)
{0 x+y = 4 | (equation 2)

Add 6 × (equation 2) to equation 1:
{13 x+0 y = 26 | (equation 1)
{0 x+y = 4 | (equation 2)

Divide equation 1 by 13:
{x+0 y = 2 | (equation 1)
{0 x+y = 4 | (equation 2)

Collect results:

Answer: {x = 2 {y = 4

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Stels [109]

1) $(-2x+4)+(x-6)$ is simplified into $=-x-2$

2) $(uv-3)+(4uv+1)$ is simplified into $5uv-2\\$

3) $(11x-8)-(2x+3)$ is simplified into $-9x-11$

4) $(x^2-4)-(x-2)$ is simplified into $x^2-x-2$

5) $(12-3t-7t^2)+(1+3t-t^2)$ is simplified into $-8t^2+13$

Step-by-step explanation:

We need to solve the polynomials.

1) $(-2x+4)+(x-6)$

Solving:

$(-2x+4)+(x-6)\\=-2x+4+x-6\\Combining\,\,like\,\,terms:\\=-2x+x+4-6\\=-x-2$

So, $(-2x+4)+(x-6)$ is simplified into $=-x-2$

2) $(uv-3)+(4uv+1)$

Solving:

$(uv-3)+(4uv+1)$

Expanding:

$=uv-3+4uv+1\\Combining\,\,like\,\,terms:\\=uv+4uv-3+1\\=5uv-2\\$

So, $(uv-3)+(4uv+1)$ is simplified into $5uv-2\\$

3) $(11x-8)-(2x+3)$

Solving:

$(11x-8)-(2x+3)$

Expanding:

$=11x-8-2x-3\\Combining\,\,like\,\,terms:\,\,\\=11x-2x-8-3\\=-9x-11$

So, $(11x-8)-(2x+3)$ is simplified into $-9x-11$

4) $(x^2-4)-(x-2)$

Solving:

$(x^2-4)-(x-2)$

Expanding:

$=x^2-4-x+2\\Combining\,\,like\,\,terms:\\=x^2-x-4+2\\=x^2-x-2$

SO, $(x^2-4)-(x-2)$ is simplified into $x^2-x-2$

5) $(12-3t-7t^2)+(1+3t-t^2)$

Solving:

$(12-3t-7t^2)+(1+3t-t^2)$

Expanding:

$=12-3t-7t^2+1+3t-t^2\\Combining\,\,like\,\,terms:\\=12+1-3t+3t-7t^2-t^2\\=13+0t-8t^2\\=-8t^2+13$

So, $(12-3t-7t^2)+(1+3t-t^2)$ is simplified into $-8t^2+13$

Keywords: Solving Polynomials

Learn more about solving Polynomials at:

#learnwithBrainly

5 0

2 years ago

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